Initial commit
This commit is contained in:
Ian Jauslin
commit
01f47ace67
54
Makefile
Normal file
54
Makefile
Normal file
@ -0,0 +1,54 @@
|
||||
PROJECTNAME=nstrophy
|
||||
VERSION=0.0
|
||||
|
||||
#DB= -ggdb
|
||||
OPT= -O3
|
||||
|
||||
WARNINGS=-Wall -Wextra -Wno-strict-overflow -std=c99 -Wpedantic
|
||||
|
||||
PREFIX=/usr
|
||||
BINDIR=$(PREFIX)/bin
|
||||
MANDIR=$(PREFIX)/share/man/man1
|
||||
|
||||
CC=/usr/bin/gcc
|
||||
LD=$(CC)
|
||||
|
||||
#INCLUDES =
|
||||
|
||||
#LIBDIRS =
|
||||
LIBS = -lm -lfftw3
|
||||
|
||||
|
||||
override LDFLAGS +=$(LIBDIRS)$(LIBS)
|
||||
override CFLAGS +=$(INCLUDES)$(DB)
|
||||
|
||||
override CFLAGS +=$(OPT) $(WARNINGS)
|
||||
|
||||
BUILDDIR=./build
|
||||
SRCDIR=./src
|
||||
|
||||
OBJS=$(patsubst %.c,%.o,$(wildcard $(SRCDIR)/*.c))
|
||||
|
||||
all: dist
|
||||
|
||||
$(PROJECTNAME): $(OBJS)
|
||||
$(LD) -o $@ $^ $(LDFLAGS)
|
||||
|
||||
%.o: %.c
|
||||
$(CC) -c $(CFLAGS) $< -o $@
|
||||
|
||||
dist: $(PROJECTNAME)
|
||||
/bin/rm -rf $(BUILDDIR)
|
||||
/bin/mkdir $(BUILDDIR)
|
||||
/bin/cp $(PROJECTNAME) $(BUILDDIR)
|
||||
@rm -f $(SRCDIR)/*.o
|
||||
@rm -f $(PROJECTNAME)
|
||||
|
||||
install: dist
|
||||
install -Dm755 $(BUILDDIR)/$(PROJECTNAME) $(BINDIR)/$(PROJECTNAME)
|
||||
install -Dm644 man/$(PROJECTNAME).1.gz $(MANDIR)/$(PROJECTNAME).1.gz
|
||||
|
||||
clean:
|
||||
@rm -f $(SRCDIR)/*.o
|
||||
@rm -rf $(BUILDDIR)
|
||||
@rm -f $(PROJECTNAME)
|
||||
70
docs/nstrophy_doc/Makefile
Normal file
70
docs/nstrophy_doc/Makefile
Normal file
@ -0,0 +1,70 @@
|
||||
PROJECTNAME=$(basename $(wildcard *.tex))
|
||||
LIBS=$(notdir $(wildcard libs/*))
|
||||
FIGS=$(notdir $(wildcard figs/*.fig))
|
||||
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
|
||||
|
||||
all: $(PROJECTNAME)
|
||||
|
||||
$(PROJECTNAME): $(LIBS) $(FIGS)
|
||||
pdflatex -file-line-error $@.tex
|
||||
pdflatex -file-line-error $@.tex
|
||||
pdflatex -synctex=1 $@.tex
|
||||
|
||||
$(PROJECTNAME).aux: $(LIBS) $(FIGS)
|
||||
pdflatex -file-line-error -draftmode $(PROJECTNAME).tex
|
||||
|
||||
|
||||
$(SYNCTEXS): $(LIBS) $(FIGS)
|
||||
pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
|
||||
|
||||
install: $(PROJECTNAME)
|
||||
cp $^.pdf $(INSTALLDIR)/
|
||||
|
||||
install-synctex: $(SYNCTEXS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
install-bibliography: bibliography/bibliography.tex
|
||||
cp bibliography/bibliography.tex $(INSTALLDIR)/bibliography/
|
||||
|
||||
|
||||
libs: $(LIBS)
|
||||
|
||||
$(LIBS):
|
||||
ln -fs libs/$@ ./
|
||||
|
||||
bibliography/bibliography.tex: $(PROJECTNAME).aux
|
||||
BBlog -c bibliography/conf.BBlog -d $(BIBLIOGRAPHY) -b bibliography/bibliography.tex
|
||||
|
||||
figs: $(FIGS)
|
||||
|
||||
$(FIGS):
|
||||
make -C figs/$@
|
||||
ln -fs figs/$@/*.pdf ./
|
||||
|
||||
|
||||
clean-aux: clean-figs-aux
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .out, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .toc, $(PROJECTNAME))
|
||||
|
||||
clean-libs:
|
||||
rm -f $(LIBS)
|
||||
|
||||
clean-figs:
|
||||
$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; )
|
||||
rm -f $(notdir $(wildcard figs/*.fig/*.pdf))
|
||||
|
||||
clean-figs-aux:
|
||||
$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
|
||||
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS) $(SYNCTEXS)
|
||||
|
||||
clean-bibliography:
|
||||
rm -f bibliography/bibliography.tex
|
||||
|
||||
clean: clean-aux clean-tex clean-libs clean-figs
|
||||
5
docs/nstrophy_doc/bibliography/conf.BBlog
Normal file
5
docs/nstrophy_doc/bibliography/conf.BBlog
Normal file
@ -0,0 +1,5 @@
|
||||
format: \bibitem[%token%]{%citeref%}%author:auth% - {\it %title%}, %journal%, %year%|doi?,\par\penalty10000%n%doi:{\tt\color{blue}\href{http://dx.doi.org/%doi%}{%doi%}}||arxiv?, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/%arxiv%}{%arxiv%}}|.\par\medskip%n% %n%
|
||||
out_file: bibliography.tex
|
||||
filter:auth: s/([A-Z])[^, ]* /\1. /g; s/ ([^ ,]*),/_\1,_/g; s/ ([^ ,]*)$/_\1/g; s/ //g; s/_/ /g;
|
||||
filter:journal: s/([a-zA-Z]) ([0-9]+)/\1~\\-\2/g;
|
||||
aux_cmd: \\citation{
|
||||
659
docs/nstrophy_doc/libs/ian.cls
Normal file
659
docs/nstrophy_doc/libs/ian.cls
Normal file
@ -0,0 +1,659 @@
|
||||
%%
|
||||
%% Ian's class file
|
||||
%%
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% class name
|
||||
\ProvidesClass{ian}[2017/09/29]
|
||||
|
||||
%% boolean to signal that this class is being used
|
||||
\newif\ifianclass
|
||||
|
||||
%% options
|
||||
% no section numbering in equations
|
||||
\DeclareOption{section_in_eq}{\sectionsineqtrue}
|
||||
\DeclareOption{section_in_fig}{\sectionsinfigtrue}
|
||||
\DeclareOption{section_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{section_in_all}{\sectionsineqtrue\sectionsinfigtrue\PassOptionsToPackage{section_in_theo}{iantheo}}
|
||||
\DeclareOption{subsection_in_eq}{\subsectionsineqtrue}
|
||||
\DeclareOption{subsection_in_fig}{\subsectionsinfigtrue}
|
||||
\DeclareOption{subsection_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{subsection_in_all}{\subsectionsineqtrue\subsectionsinfigtrue\PassOptionsToPackage{subsection_in_theo}{iantheo}}
|
||||
\DeclareOption{no_section_in_eq}{\sectionsineqfalse}
|
||||
\DeclareOption{no_section_in_fig}{\sectionsinfigfalse}
|
||||
\DeclareOption{no_section_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{no_section_in_all}{\sectionsineqfalse\sectionsinfigfalse\PassOptionsToPackage{no_section_in_theo}{iantheo}}
|
||||
\DeclareOption{no_subsection_in_eq}{\subsectionsineqfalse}
|
||||
\DeclareOption{no_subsection_in_fig}{\subsectionsinfigfalse}
|
||||
\DeclareOption{no_subsection_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{no_subsection_in_all}{\subsectionsineqfalse\subsectionsinfigfalse\PassOptionsToPackage{no_subsection_in_theo}{iantheo}}
|
||||
% reset point
|
||||
\DeclareOption{point_reset_at_section}{\PassOptionsToPackage{reset_at_section}{point}}
|
||||
\DeclareOption{point_no_reset_at_section}{\PassOptionsToPackage{no_reset_at_section}{point}}
|
||||
\DeclareOption{point_reset_at_theo}{\PassOptionsToPackage{reset_at_theo}{point}}
|
||||
\DeclareOption{point_no_reset_at_theo}{\PassOptionsToPackage{no_reset_at_theo}{point}}
|
||||
|
||||
\def\ian@defaultoptions{
|
||||
\ExecuteOptions{section_in_all, no_subsection_in_all}
|
||||
\ProcessOptions
|
||||
|
||||
%% required packages
|
||||
\RequirePackage{iantheo}
|
||||
\RequirePackage{point}
|
||||
\RequirePackage{color}
|
||||
\RequirePackage{marginnote}
|
||||
\RequirePackage{amssymb}
|
||||
\PassOptionsToPackage{hidelinks}{hyperref}
|
||||
\RequirePackage{hyperref}
|
||||
}
|
||||
|
||||
%% paper dimensions
|
||||
\setlength\paperheight{297mm}
|
||||
\setlength\paperwidth{210mm}
|
||||
|
||||
%% fonts
|
||||
\input{size11.clo}
|
||||
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
|
||||
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
|
||||
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
|
||||
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
|
||||
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
|
||||
|
||||
%% text dimensions
|
||||
\hoffset=-50pt
|
||||
\voffset=-72pt
|
||||
\textwidth=460pt
|
||||
\textheight=704pt
|
||||
|
||||
|
||||
%% remove default indentation
|
||||
\parindent=0pt
|
||||
%% indent command
|
||||
\def\indent{\hskip20pt}
|
||||
|
||||
%% something is wrong with \thepage, redefine it
|
||||
\gdef\thepage{\the\c@page}
|
||||
|
||||
%% array lines (to use the array environment)
|
||||
\setlength\arraycolsep{5\p@}
|
||||
\setlength\arrayrulewidth{.4\p@}
|
||||
|
||||
|
||||
%% correct vertical alignment at the end of a document
|
||||
\AtEndDocument{
|
||||
\vfill
|
||||
\eject
|
||||
}
|
||||
|
||||
|
||||
%% hyperlinks
|
||||
% hyperlinkcounter
|
||||
\newcounter{lncount}
|
||||
% hyperref anchor
|
||||
\def\hrefanchor{%
|
||||
\stepcounter{lncount}%
|
||||
\hypertarget{ln.\thelncount}{}%
|
||||
}
|
||||
|
||||
%% define a command and write it to aux file
|
||||
\def\outdef#1#2{%
|
||||
% define command%
|
||||
\expandafter\xdef\csname #1\endcsname{#2}%
|
||||
% hyperlink number%
|
||||
\expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
|
||||
% write command to aux%
|
||||
\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
|
||||
\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
|
||||
}
|
||||
|
||||
%% can call commands even when they are not defined
|
||||
\def\safe#1{%
|
||||
\ifdefined#1%
|
||||
#1%
|
||||
\else%
|
||||
{\color{red}\bf?}%
|
||||
\fi%
|
||||
}
|
||||
|
||||
%% define a label for the latest tag
|
||||
%% label defines a command containing the string stored in \tag
|
||||
\def\deflabel{
|
||||
\def\label##1{\expandafter\outdef{label@##1}{\safe\tag}}
|
||||
|
||||
\def\ref##1{%
|
||||
% check whether the label is defined (hyperlink runs into errors if this check is omitted)
|
||||
\ifcsname label@##1@hl\endcsname%
|
||||
\hyperlink{ln.\csname label@##1@hl\endcsname}{{\color{blue}\safe\csname label@##1\endcsname}}%
|
||||
\else%
|
||||
\ifcsname label@##1\endcsname%
|
||||
{\color{blue}\csname ##1\endcsname}%
|
||||
\else%
|
||||
{\bf ??}%
|
||||
\fi%
|
||||
\fi%
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
%% make a custom link at any given location in the document
|
||||
\def\makelink#1#2{%
|
||||
\hrefanchor%
|
||||
\outdef{label@#1}{#2}%
|
||||
}
|
||||
|
||||
|
||||
%% section command
|
||||
% counter
|
||||
\newcounter{sectioncount}
|
||||
% space before section
|
||||
\newlength\secskip
|
||||
\setlength\secskip{40pt}
|
||||
% a prefix to put before the section number, e.g. A for appendices
|
||||
\def\sectionprefix{}
|
||||
% define some lengths
|
||||
\newlength\secnumwidth
|
||||
\newlength\sectitlewidth
|
||||
\def\section#1{
|
||||
% reset counters
|
||||
\stepcounter{sectioncount}
|
||||
\setcounter{subsectioncount}{0}
|
||||
\ifsectionsineq
|
||||
\setcounter{seqcount}0
|
||||
\fi
|
||||
\ifsectionsinfig
|
||||
\setcounter{figcount}0
|
||||
\fi
|
||||
|
||||
% space before section (if not first)
|
||||
\ifnum\thesectioncount>1
|
||||
\vskip\secskip
|
||||
\penalty-1000
|
||||
\fi
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\sectionprefix\thesectioncount}
|
||||
|
||||
% get widths
|
||||
\def\@secnum{{\bf\Large\sectionprefix\thesectioncount.\hskip10pt}}
|
||||
\settowidth\secnumwidth{\@secnum}
|
||||
\setlength\sectitlewidth\textwidth
|
||||
\addtolength\sectitlewidth{-\secnumwidth}
|
||||
|
||||
% print name
|
||||
\parbox{\textwidth}{
|
||||
\@secnum
|
||||
\parbox[t]{\sectitlewidth}{\Large\bf #1}}
|
||||
|
||||
% write to table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@sec.\thesectioncount\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocsection{#1}{\thepage}}
|
||||
\fi
|
||||
|
||||
%space
|
||||
\par\penalty10000
|
||||
\bigskip\penalty10000
|
||||
}
|
||||
|
||||
%% subsection
|
||||
% counter
|
||||
\newcounter{subsectioncount}
|
||||
% space before subsection
|
||||
\newlength\subsecskip
|
||||
\setlength\subsecskip{30pt}
|
||||
\def\subsection#1{
|
||||
% counters
|
||||
\stepcounter{subsectioncount}
|
||||
\setcounter{subsubsectioncount}{0}
|
||||
\ifsubsectionsineq
|
||||
\setcounter{seqcount}0
|
||||
\fi
|
||||
\ifsubsectionsinfig
|
||||
\setcounter{figcount}0
|
||||
\fi
|
||||
|
||||
% space before subsection (if not first)
|
||||
\ifnum\thesubsectioncount>1
|
||||
\vskip\subsecskip
|
||||
\penalty-500
|
||||
\fi
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount}
|
||||
|
||||
% get widths
|
||||
\def\@secnum{{\bf\large\hskip.5cm\sectionprefix\thesectioncount.\thesubsectioncount.\hskip5pt}}
|
||||
\settowidth\secnumwidth{\@secnum}
|
||||
\setlength\sectitlewidth\textwidth
|
||||
\addtolength\sectitlewidth{-\secnumwidth}
|
||||
% print name
|
||||
\parbox{\textwidth}{
|
||||
\@secnum
|
||||
\parbox[t]{\sectitlewidth}{\large\bf #1}}
|
||||
|
||||
% write to table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsec.\thesectioncount.\thesubsectioncount\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocsubsection{#1}{\thepage}}
|
||||
\fi
|
||||
|
||||
% space
|
||||
\par\penalty10000
|
||||
\medskip\penalty10000
|
||||
}
|
||||
|
||||
%% subsubsection
|
||||
% counter
|
||||
\newcounter{subsubsectioncount}
|
||||
% space before subsubsection
|
||||
\newlength\subsubsecskip
|
||||
\setlength\subsubsecskip{20pt}
|
||||
\def\subsubsection#1{
|
||||
% counters
|
||||
\stepcounter{subsubsectioncount}
|
||||
|
||||
% space before subsubsection (if not first)
|
||||
\ifnum\thesubsubsectioncount>1
|
||||
\vskip\subsubsecskip
|
||||
\penalty-500
|
||||
\fi
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount}
|
||||
|
||||
% get widths
|
||||
\def\@secnum{{\bf\hskip1.cm\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount.\hskip5pt}}
|
||||
\settowidth\secnumwidth{\@secnum}
|
||||
\setlength\sectitlewidth\textwidth
|
||||
\addtolength\sectitlewidth{-\secnumwidth}
|
||||
% print name
|
||||
\parbox{\textwidth}{
|
||||
\@secnum
|
||||
\parbox[t]{\sectitlewidth}{\large\bf #1}}
|
||||
|
||||
% write to table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsubsec.\thesectioncount.\thesubsectioncount.\thesubsubsectioncount\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocsubsubsection{#1}{\thepage}}
|
||||
\fi
|
||||
|
||||
% space
|
||||
\par\penalty10000
|
||||
\medskip\penalty10000
|
||||
}
|
||||
|
||||
%% itemize
|
||||
\newlength\itemizeskip
|
||||
% left margin for items
|
||||
\setlength\itemizeskip{20pt}
|
||||
\newlength\itemizeseparator
|
||||
% space between the item symbol and the text
|
||||
\setlength\itemizeseparator{5pt}
|
||||
% penalty preceding an itemize
|
||||
\newcount\itemizepenalty
|
||||
\itemizepenalty=0
|
||||
% counter counting the itemize level
|
||||
\newcounter{itemizecount}
|
||||
|
||||
% item symbol
|
||||
\def\itemizept#1{
|
||||
\ifnum#1=1
|
||||
\textbullet
|
||||
\else
|
||||
$\scriptstyle\blacktriangleright$
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
\newlength\current@itemizeskip
|
||||
\setlength\current@itemizeskip{0pt}
|
||||
\def\itemize{%
|
||||
\par\expandafter\penalty\the\itemizepenalty\medskip\expandafter\penalty\the\itemizepenalty%
|
||||
\addtocounter{itemizecount}{1}%
|
||||
\addtolength\current@itemizeskip{\itemizeskip}%
|
||||
\leftskip\current@itemizeskip%
|
||||
}
|
||||
\def\enditemize{%
|
||||
\addtocounter{itemizecount}{-1}%
|
||||
\addtolength\current@itemizeskip{-\itemizeskip}%
|
||||
\par\expandafter\penalty\the\itemizepenalty\leftskip\current@itemizeskip%
|
||||
\medskip\expandafter\penalty\the\itemizepenalty%
|
||||
}
|
||||
\newlength\itempt@total
|
||||
\def\item{
|
||||
\settowidth\itempt@total{\itemizept\theitemizecount}
|
||||
\addtolength\itempt@total{\itemizeseparator}
|
||||
\par
|
||||
\medskip
|
||||
\hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator
|
||||
}
|
||||
|
||||
|
||||
%% prevent page breaks after itemize
|
||||
\newcount\previtemizepenalty
|
||||
\def\nopagebreakafteritemize{
|
||||
\previtemizepenalty=\itemizepenalty
|
||||
\itemizepenalty=10000
|
||||
}
|
||||
%% back to previous value
|
||||
\def\restorepagebreakafteritemize{
|
||||
\itemizepenalty=\previtemizepenalty
|
||||
}
|
||||
|
||||
%% enumerate
|
||||
\newcounter{enumerate@count}
|
||||
\def\enumerate{
|
||||
\setcounter{enumerate@count}0
|
||||
\let\olditem\item
|
||||
\let\olditemizept\itemizept
|
||||
\def\item{
|
||||
% counter
|
||||
\stepcounter{enumerate@count}
|
||||
% set header
|
||||
\def\itemizept{\theenumerate@count.}
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\theenumerate@count}
|
||||
\olditem
|
||||
}
|
||||
\itemize
|
||||
}
|
||||
\def\endenumerate{
|
||||
\enditemize
|
||||
\let\item\olditem
|
||||
\let\itemizept\olditemizept
|
||||
}
|
||||
|
||||
|
||||
%% equation numbering
|
||||
% counter
|
||||
\newcounter{seqcount}
|
||||
% booleans (write section or subsection in equation number)
|
||||
\newif\ifsectionsineq
|
||||
\newif\ifsubsectionsineq
|
||||
\def\seqcount{
|
||||
\stepcounter{seqcount}
|
||||
% the output
|
||||
\edef\seqformat{\theseqcount}
|
||||
% add subsection number
|
||||
\ifsubsectionsineq
|
||||
\let\tmp\seqformat
|
||||
\edef\seqformat{\thesubsectioncount.\tmp}
|
||||
\fi
|
||||
% add section number
|
||||
\ifsectionsineq
|
||||
\let\tmp\seqformat
|
||||
\edef\seqformat{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\seqformat}
|
||||
% write number
|
||||
\marginnote{\hfill(\seqformat)}
|
||||
}
|
||||
%% equation environment compatibility
|
||||
\def\equation{\hrefanchor$$\seqcount}
|
||||
\def\endequation{$$\@ignoretrue}
|
||||
|
||||
|
||||
%% figures
|
||||
% counter
|
||||
\newcounter{figcount}
|
||||
% booleans (write section or subsection in equation number)
|
||||
\newif\ifsectionsinfig
|
||||
\newif\ifsubsectionsinfig
|
||||
% width of figures
|
||||
\newlength\figwidth
|
||||
\setlength\figwidth\textwidth
|
||||
\addtolength\figwidth{-2.5cm}
|
||||
% caption
|
||||
\def\defcaption{
|
||||
\long\def\caption##1{
|
||||
\stepcounter{figcount}
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
|
||||
% the number of the figure
|
||||
\edef\figformat{\thefigcount}
|
||||
% add subsection number
|
||||
\ifsubsectionsinfig
|
||||
\let\tmp\figformat
|
||||
\edef\figformat{\thesubsectioncount.\tmp}
|
||||
\fi
|
||||
% add section number
|
||||
\ifsectionsinfig
|
||||
\let\tmp\figformat
|
||||
\edef\figformat{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\figformat}
|
||||
|
||||
% write
|
||||
\hfil fig \figformat: \parbox[t]{\figwidth}{\leavevmode\small##1}
|
||||
|
||||
% space
|
||||
\par\bigskip
|
||||
}
|
||||
}
|
||||
%% short caption: centered
|
||||
\def\captionshort#1{
|
||||
\stepcounter{figcount}
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
|
||||
% the number of the figure
|
||||
\edef\figformat{\thefigcount}
|
||||
% add section number
|
||||
\ifsectionsinfig
|
||||
\let\tmp\figformat
|
||||
\edef\figformat{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\figformat}
|
||||
|
||||
% write
|
||||
\hfil fig \figformat: {\small#1}
|
||||
|
||||
%space
|
||||
\par\bigskip
|
||||
}
|
||||
|
||||
%% environment
|
||||
\def\figure{
|
||||
\par
|
||||
\vfil\penalty100\vfilneg
|
||||
\bigskip
|
||||
}
|
||||
\def\endfigure{
|
||||
\par
|
||||
\vfil\penalty100\vfilneg
|
||||
\bigskip
|
||||
}
|
||||
|
||||
|
||||
%% start appendices
|
||||
\def\appendix{
|
||||
\vfill
|
||||
\pagebreak
|
||||
|
||||
% counter
|
||||
\setcounter{sectioncount}0
|
||||
|
||||
% prefix
|
||||
\def\sectionprefix{A}
|
||||
|
||||
% write
|
||||
{\bf \LARGE Appendices}\par\penalty10000\bigskip\penalty10000
|
||||
|
||||
% add a mention in the table of contents
|
||||
\iftoc
|
||||
\immediate\write\tocoutput{\noexpand\tocappendices}\penalty10000
|
||||
\fi
|
||||
|
||||
%% uncomment for new page for each appendix
|
||||
%\def\seqskip{\vfill\pagebreak}
|
||||
}
|
||||
|
||||
|
||||
%% bibliography
|
||||
% size of header
|
||||
\newlength\bibheader
|
||||
\def\thebibliography#1{
|
||||
\hrefanchor
|
||||
|
||||
% add a mention in the table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@references\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocreferences{\thepage}}\penalty10000
|
||||
\fi
|
||||
|
||||
% write
|
||||
{\bf \LARGE References}\par\penalty10000\bigskip\penalty10000
|
||||
% width of header
|
||||
\settowidth\bibheader{[#1]}
|
||||
\leftskip\bibheader
|
||||
}
|
||||
% end environment
|
||||
\def\endthebibliography{
|
||||
\par\leftskip0pt
|
||||
}
|
||||
|
||||
%% bibitem command
|
||||
\def\bibitem[#1]#2{%
|
||||
\hrefanchor%
|
||||
\outdef{label@cite#2}{#1}%
|
||||
\hskip-\bibheader%
|
||||
\makebox[\bibheader]{\cite{#2}\hfill}%
|
||||
}
|
||||
|
||||
%% cite command (adapted from latex.ltx)
|
||||
% @tempswa is set to true when there is an optional argument
|
||||
\newif\@tempswa
|
||||
\def\cite{%
|
||||
% check whether there is an optional argument (if there is none, add on empty '[]')
|
||||
\@ifnextchar [{\@tempswatrue\@citex}{\@tempswafalse\@citex[]}%
|
||||
}
|
||||
% command with optional argument
|
||||
\def\@citex[#1]#2{\leavevmode%
|
||||
% initialize loop
|
||||
\let\@citea\@empty%
|
||||
% format
|
||||
\@cite{%
|
||||
% loop over ',' separated list
|
||||
\@for\@citeb:=#2\do{%
|
||||
% text to add at each iteration of the loop (separator between citations)
|
||||
\@citea\def\@citea{,\ }%
|
||||
% add entry to citelist
|
||||
\@writecitation{\@citeb}%
|
||||
\ref{cite\@citeb}%
|
||||
}%
|
||||
}%
|
||||
% add optional argument text (as an argument to '\@cite')
|
||||
{#1}%
|
||||
}
|
||||
\def\@cite#1#2{%
|
||||
[#1\if@tempswa , #2\fi]%
|
||||
}
|
||||
%% add entry to citelist after checking it has not already been added
|
||||
\def\@writecitation#1{%
|
||||
\ifcsname if#1cited\endcsname%
|
||||
\else%
|
||||
\expandafter\newif\csname if#1cited\endcsname%
|
||||
\immediate\write\@auxout{\string\citation{#1}}%
|
||||
\fi%
|
||||
}
|
||||
|
||||
%% table of contents
|
||||
% boolean
|
||||
\newif\iftoc
|
||||
\def\tableofcontents{
|
||||
{\bf \large Table of contents:}\par\penalty10000\bigskip\penalty10000
|
||||
|
||||
% copy content from file
|
||||
\IfFileExists{\jobname.toc}{\input{\jobname.toc}}{{\tt error: table of contents missing}}
|
||||
|
||||
% open new toc
|
||||
\newwrite\tocoutput
|
||||
\immediate\openout\tocoutput=\jobname.toc
|
||||
|
||||
\toctrue
|
||||
}
|
||||
%% close file
|
||||
\AtEndDocument{
|
||||
% close toc
|
||||
\iftoc
|
||||
\immediate\closeout\tocoutput
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
%% fill line with dots
|
||||
\def\leaderfill{\leaders\hbox to 1em {\hss. \hss}\hfill}
|
||||
|
||||
%% same as sectionprefix
|
||||
\def\tocsectionprefix{}
|
||||
|
||||
%% toc formats
|
||||
\newcounter{tocsectioncount}
|
||||
\def\tocsection #1#2{
|
||||
\stepcounter{tocsectioncount}
|
||||
\setcounter{tocsubsectioncount}{0}
|
||||
\setcounter{tocsubsubsectioncount}{0}
|
||||
% write
|
||||
\smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt {\color{blue}#1}\leaderfill#2}\par
|
||||
}
|
||||
\newcounter{tocsubsectioncount}
|
||||
\def\tocsubsection #1#2{
|
||||
\stepcounter{tocsubsectioncount}
|
||||
\setcounter{tocsubsubsectioncount}{0}
|
||||
% write
|
||||
{\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
|
||||
}
|
||||
\newcounter{tocsubsubsectioncount}
|
||||
\def\tocsubsubsection #1#2{
|
||||
\stepcounter{tocsubsubsectioncount}
|
||||
% write
|
||||
{\hskip20pt\hyperlink{ln.\csname toc@subsubsec.\thetocsectioncount.\thetocsubsectioncount.\thetocsubsubsectioncount\endcsname}{{\bf \thetocsubsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
|
||||
}
|
||||
\def\tocappendices{
|
||||
\medskip
|
||||
\setcounter{tocsectioncount}0
|
||||
{\bf Appendices}\par
|
||||
\smallskip
|
||||
\def\tocsectionprefix{A}
|
||||
}
|
||||
\def\tocreferences#1{
|
||||
\medskip
|
||||
{\hyperlink{ln.\csname toc@references\endcsname}{{\color{blue}\bf References}\leaderfill#1}}\par
|
||||
\smallskip
|
||||
}
|
||||
|
||||
|
||||
%% definitions that must be loaded at begin document
|
||||
\let\ian@olddocument\document
|
||||
\def\document{
|
||||
\ian@olddocument
|
||||
|
||||
\deflabel
|
||||
\defcaption
|
||||
}
|
||||
|
||||
%% end
|
||||
\ian@defaultoptions
|
||||
\endinput
|
||||
162
docs/nstrophy_doc/libs/iantheo.sty
Normal file
162
docs/nstrophy_doc/libs/iantheo.sty
Normal file
@ -0,0 +1,162 @@
|
||||
%%
|
||||
%% iantheorem package:
|
||||
%% Ian's customized theorem command
|
||||
%%
|
||||
|
||||
%% boolean to signal that this package was loaded
|
||||
\newif\ifiantheo
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% package name
|
||||
\ProvidesPackage{iantheo}[2016/11/10]
|
||||
|
||||
%% options
|
||||
\newif\ifsectionintheo
|
||||
\DeclareOption{section_in_theo}{\sectionintheotrue}
|
||||
\DeclareOption{no_section_in_theo}{\sectionintheofalse}
|
||||
\newif\ifsubsectionintheo
|
||||
\DeclareOption{subsection_in_theo}{\subsectionintheotrue}
|
||||
\DeclareOption{no_subsection_in_theo}{\subsectionintheofalse}
|
||||
|
||||
\def\iantheo@defaultoptions{
|
||||
\ExecuteOptions{section_in_theo, no_subsection_in_theo}
|
||||
\ProcessOptions
|
||||
|
||||
%%% reset at every new section
|
||||
\ifsectionintheo
|
||||
\let\iantheo@oldsection\section
|
||||
\gdef\section{\setcounter{theocount}{0}\iantheo@oldsection}
|
||||
\fi
|
||||
|
||||
%% reset at every new subsection
|
||||
\ifsubsectionintheo
|
||||
\let\iantheo@oldsubsection\subsection
|
||||
\gdef\subsection{\setcounter{theocount}{0}\iantheo@oldsubsection}
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
%% delimiters
|
||||
\def\delimtitle#1{
|
||||
\par%
|
||||
\leavevmode%
|
||||
\raise.3em\hbox to\hsize{%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
\hrulefill%
|
||||
\ \lower.3em\hbox{#1}\ %
|
||||
\hrulefill%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
}%
|
||||
\par\penalty10000%
|
||||
}
|
||||
|
||||
%% callable by ref
|
||||
\def\delimtitleref#1{
|
||||
\par%
|
||||
%
|
||||
\ifdefined\ianclass%
|
||||
% hyperref anchor%
|
||||
\hrefanchor%
|
||||
% define tag (for \label)%
|
||||
\xdef\tag{#1}%
|
||||
\fi%
|
||||
%
|
||||
\leavevmode%
|
||||
\raise.3em\hbox to\hsize{%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
\hrulefill%
|
||||
\ \lower.3em\hbox{\bf #1}\ %
|
||||
\hrulefill%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
}%
|
||||
\par\penalty10000%
|
||||
}
|
||||
|
||||
%% no title
|
||||
\def\delim{
|
||||
\par%
|
||||
\leavevmode\raise.3em\hbox to\hsize{%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
\hrulefill%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
}%
|
||||
\par\penalty10000%
|
||||
}
|
||||
|
||||
%% end delim
|
||||
\def\enddelim{
|
||||
\par\penalty10000%
|
||||
\leavevmode%
|
||||
\raise.3em\hbox to\hsize{%
|
||||
\vrule height0.3em\hrulefill\vrule height0.3em%
|
||||
}%
|
||||
\par%
|
||||
}
|
||||
|
||||
|
||||
%% theorem
|
||||
% counter
|
||||
\newcounter{theocount}
|
||||
% booleans (write section or subsection in equation number)
|
||||
\def\theo#1{
|
||||
\stepcounter{theocount}
|
||||
\ifdefined\ianclass
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
\fi
|
||||
% the number
|
||||
\def\formattheo{\thetheocount}
|
||||
% add subsection number
|
||||
\ifsubsectionintheo
|
||||
\let\tmp\formattheo
|
||||
\edef\formattheo{\thesubsectioncount.\tmp}
|
||||
\fi
|
||||
% add section number
|
||||
\ifsectionintheo
|
||||
\let\tmp\formattheo
|
||||
\edef\formattheo{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\formattheo}
|
||||
% write
|
||||
\delimtitle{\bf #1 \formattheo}
|
||||
}
|
||||
\let\endtheo\enddelim
|
||||
%% theorem headers with name
|
||||
\def\theoname#1#2{
|
||||
\theo{#1}\hfil({\it #2})\par\penalty10000\medskip%
|
||||
}
|
||||
|
||||
|
||||
%% qed symbol
|
||||
\def\qedsymbol{$\square$}
|
||||
\def\qed{\penalty10000\hfill\penalty10000\qedsymbol}
|
||||
|
||||
|
||||
%% compatibility with article class
|
||||
\ifdefined\ianclasstrue
|
||||
\relax
|
||||
\else
|
||||
\def\thesectioncount{\thesection}
|
||||
\def\thesubsectioncount{\thesubsection}
|
||||
\def\sectionprefix{}
|
||||
\fi
|
||||
|
||||
|
||||
%% prevent page breaks after displayed equations
|
||||
\newcount\prevpostdisplaypenalty
|
||||
\def\nopagebreakaftereq{
|
||||
\prevpostdisplaypenalty=\postdisplaypenalty
|
||||
\postdisplaypenalty=10000
|
||||
}
|
||||
%% back to previous value
|
||||
\def\restorepagebreakaftereq{
|
||||
\postdisplaypenalty=\prevpostdisplaypenalty
|
||||
}
|
||||
|
||||
|
||||
%% end
|
||||
\iantheo@defaultoptions
|
||||
\endinput
|
||||
19
docs/nstrophy_doc/libs/largearray.sty
Normal file
19
docs/nstrophy_doc/libs/largearray.sty
Normal file
@ -0,0 +1,19 @@
|
||||
%%
|
||||
%% largearray package:
|
||||
%% Array spanning the entire line
|
||||
%%
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% package name
|
||||
\ProvidesPackage{largearray}[2016/11/10]
|
||||
|
||||
\RequirePackage{array}
|
||||
|
||||
%% array spanning the entire line
|
||||
\newlength\largearray@width
|
||||
\setlength\largearray@width\textwidth
|
||||
\addtolength\largearray@width{-10pt}
|
||||
\def\largearray{\begin{array}{@{}>{\displaystyle}l@{}}\hphantom{\hspace{\largearray@width}}\\[-.5cm]}
|
||||
\def\endlargearray{\end{array}}
|
||||
106
docs/nstrophy_doc/libs/point.sty
Normal file
106
docs/nstrophy_doc/libs/point.sty
Normal file
@ -0,0 +1,106 @@
|
||||
%%
|
||||
%% Points package:
|
||||
%% \point commands
|
||||
%%
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% package name
|
||||
\ProvidesPackage{point}[2017/06/13]
|
||||
|
||||
%% options
|
||||
\newif\ifresetatsection
|
||||
\DeclareOption{reset_at_section}{\resetatsectiontrue}
|
||||
\DeclareOption{no_reset_at_section}{\resetatsectionfalse}
|
||||
\newif\ifresetatsubsection
|
||||
\DeclareOption{reset_at_subsection}{\resetatsubsectiontrue}
|
||||
\DeclareOption{no_reset_at_subsection}{\resetatsubsectionfalse}
|
||||
\newif\ifresetattheo
|
||||
\DeclareOption{reset_at_theo}{\resetattheotrue}
|
||||
\DeclareOption{no_reset_at_theo}{\resetattheofalse}
|
||||
|
||||
\def\point@defaultoptions{
|
||||
\ExecuteOptions{reset_at_section, reset_at_subsection, no_reset_at_theo}
|
||||
\ProcessOptions
|
||||
|
||||
%% reset at every new section
|
||||
\ifresetatsection
|
||||
\let\point@oldsection\section
|
||||
\gdef\section{\resetpointcounter\point@oldsection}
|
||||
\fi
|
||||
%% reset at every new subsection
|
||||
\ifresetatsubsection
|
||||
\let\point@oldsubsection\subsection
|
||||
\gdef\subsection{\resetpointcounter\point@oldsubsection}
|
||||
\fi
|
||||
|
||||
%% reset at every new theorem
|
||||
\ifresetattheo
|
||||
\ifdefined\iantheotrue
|
||||
\let\point@oldtheo\theo
|
||||
\gdef\theo{\resetpointcounter\point@oldtheo}
|
||||
\fi
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
%% point
|
||||
% counter
|
||||
\newcounter{pointcount}
|
||||
\def\point{
|
||||
\stepcounter{pointcount}
|
||||
\setcounter{subpointcount}{0}
|
||||
% hyperref anchor (only if the class is 'ian')
|
||||
\ifdefined\ifianclass
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\thepointcount}
|
||||
\fi
|
||||
% header
|
||||
\indent{\bf \thepointcount\ - }
|
||||
}
|
||||
|
||||
%% subpoint
|
||||
% counter
|
||||
\newcounter{subpointcount}
|
||||
\def\subpoint{
|
||||
\stepcounter{subpointcount}
|
||||
\setcounter{subsubpointcount}0
|
||||
% hyperref anchor (only if the class is 'ian')
|
||||
\ifdefined\ifianclass
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\thepointcount-\thesubpointcount}
|
||||
\fi
|
||||
% header
|
||||
\indent\hskip.5cm{\bf \thepointcount-\thesubpointcount\ - }
|
||||
}
|
||||
|
||||
%% subsubpoint
|
||||
% counter
|
||||
\newcounter{subsubpointcount}
|
||||
\def\subsubpoint{
|
||||
\stepcounter{subsubpointcount}
|
||||
% hyperref anchor (only if the class is 'ian')
|
||||
\ifdefined\ifianclass
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\thepointcount-\thesubpointcount-\thesubsubpointcount}
|
||||
\fi
|
||||
\indent\hskip1cm{\bf \thepointcount-\thesubpointcount-\thesubsubpointcount\ - }
|
||||
}
|
||||
|
||||
|
||||
%% reset point counters
|
||||
\def\resetpointcounter{
|
||||
\setcounter{pointcount}{0}
|
||||
\setcounter{subpointcount}{0}
|
||||
\setcounter{subsubpointcount}{0}
|
||||
}
|
||||
|
||||
|
||||
|
||||
%% end
|
||||
\point@defaultoptions
|
||||
\endinput
|
||||
146
docs/nstrophy_doc/nstrophy_doc.tex
Normal file
146
docs/nstrophy_doc/nstrophy_doc.tex
Normal file
@ -0,0 +1,146 @@
|
||||
\documentclass{ian}
|
||||
|
||||
\usepackage{largearray}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\hbox{}
|
||||
\hfil{\bf\LARGE
|
||||
{\tt nstrophy}
|
||||
}
|
||||
\vfill
|
||||
|
||||
\tableofcontents
|
||||
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\setcounter{page}1
|
||||
\pagestyle{plain}
|
||||
|
||||
\section{Description of the computation}
|
||||
\subsection{Irreversible equation}
|
||||
\indent Consider the {\it irreversible} Navier-Stokes equation in 2 dimensions
|
||||
\begin{equation}
|
||||
\partial_tu=\nu\Delta u+g-\nabla w-(u\cdot\nabla)u,\quad
|
||||
\nabla\cdot u=0
|
||||
\label{ins}
|
||||
\end{equation}
|
||||
in which $g$ is the forcing term and $w$ is the pressure.
|
||||
We take periodic boundary conditions, so, at every given time, $u(t,\cdot)$ is a function on the unit torus $\mathbb T^2:=\mathbb R^2/\mathbb Z^2$. We represent $u(t,\cdot)$ using its Fourier series
|
||||
\begin{equation}
|
||||
\hat u_k(t):=\int_{\mathbb T^2}dx\ e^{2i\pi kx}u(t,x)
|
||||
\end{equation}
|
||||
for $k\in\mathbb Z^2$, and rewrite~\-(\ref{ins}) as
|
||||
\begin{equation}
|
||||
\partial_t\hat u_k=
|
||||
-4\pi^2\nu k^2\hat u_k+\hat g_k-2i\pi k\hat w_k
|
||||
-2i\pi\sum_{\displaystyle\mathop{\scriptstyle p,q\in\mathbb Z^2}_{p+q=k}}
|
||||
(q\cdot\hat u_p)\hat u_q
|
||||
,\quad
|
||||
k\cdot\hat u_k=0
|
||||
\label{ins_k}
|
||||
\end{equation}
|
||||
We then reduce the equation to a scalar one, by writing
|
||||
\begin{equation}
|
||||
\hat u_k=\frac{2i\pi k^\perp}{|k|}\hat\varphi_k\equiv\frac{2i\pi}{|k|}(-k_y\hat\varphi_k,k_x\hat\varphi_k)
|
||||
\end{equation}
|
||||
in terms of which, multiplying both sides of the equation by $\frac{k^\perp}{|k|}$,
|
||||
\begin{equation}
|
||||
\partial_t\hat \varphi_k=
|
||||
-4\pi^2\nu k^2\hat \varphi_k+\frac{k^\perp}{2i\pi|k|}\cdot\hat g_k
|
||||
-\frac{2i\pi}{|k|}\sum_{\displaystyle\mathop{\scriptstyle p,q\in\mathbb Z^2}_{p+q=k}}
|
||||
(q\cdot p^\perp)(k^\perp\cdot q^\perp)\hat\varphi_p\hat\varphi_q
|
||||
\label{ins_k}
|
||||
\end{equation}
|
||||
which, since $q\cdot p^\perp=q\cdot(k^\perp-q^\perp)=q\cdot k^\perp$, is
|
||||
\begin{equation}
|
||||
\partial_t\hat \varphi_k=
|
||||
-4\pi^2\nu k^2\hat \varphi_k+\frac{k^\perp}{2i\pi|k|}\cdot\hat g_k
|
||||
+\frac{4\pi^2}{|k|}\sum_{\displaystyle\mathop{\scriptstyle p,q\in\mathbb Z^2}_{p+q=k}}
|
||||
(q\cdot k^\perp)(k\cdot q)\frac{\hat\varphi_p\hat\varphi_q}{|p||q|}
|
||||
.
|
||||
\label{ins_k}
|
||||
\end{equation}
|
||||
We truncate the Fourier modes and assume that $\hat\varphi_k=0$ if $|k_1|>K_1$ or $|k_2|>K_2$. Let
|
||||
\begin{equation}
|
||||
\mathcal K:=\{(k_1,k_2),\ |k_1|\leqslant K_1,\ |k_2|\leqslant K_2\}
|
||||
.
|
||||
\end{equation}
|
||||
\bigskip
|
||||
|
||||
\point{\bf FFT}. We compute the last term in~\-(\ref{ins_k})
|
||||
\begin{equation}
|
||||
T(\hat\varphi,k):=
|
||||
\sum_{\displaystyle\mathop{\scriptstyle p,q\in\mathbb Z^2}_{p+q=k}}
|
||||
\frac{\hat\varphi_p}{|p|}
|
||||
(q\cdot k^\perp)(k\cdot q)\frac{\hat\varphi_q}{|q|}
|
||||
\end{equation}
|
||||
using a fast Fourier transform, defined as
|
||||
\begin{equation}
|
||||
\mathcal F(f)(n):=\sum_{m\in\mathcal N}e^{-\frac{2i\pi}{N_1}m_1n_1-\frac{2i\pi}{N_2}m_2n_2}f(m_1,m_2)
|
||||
\end{equation}
|
||||
where
|
||||
\begin{equation}
|
||||
\mathcal N:=\{(n_1,n_2),\ 0\leqslant n_1\leqslant N_1,\ 0\leqslant n_2\leqslant N_2\}
|
||||
\end{equation}
|
||||
for some fixed $N_1,N_2$. The transform is inverted by
|
||||
\begin{equation}
|
||||
\frac1{N_1N_2}\mathcal F^*(\mathcal F(f))(n)=f(n)
|
||||
\end{equation}
|
||||
in which $\mathcal F^*$ is defined like $\mathcal F$ but with the opposite phase.
|
||||
\bigskip
|
||||
|
||||
\indent The condition $p+q=k$ can be rewritten as
|
||||
\begin{equation}
|
||||
T(\hat\varphi,k)
|
||||
=
|
||||
\sum_{p,q\in\mathcal K}
|
||||
\frac1{N_1N_2}
|
||||
\sum_{n\in\mathcal N}e^{-\frac{2i\pi}{N_1}n_1(p_1+q_1-k_1)-\frac{2i\pi}{N_2}n_2(p_2+q_2-k_2)}
|
||||
\frac{\hat\varphi_p}{|p|}
|
||||
(q\cdot k^\perp)(k\cdot q)\frac{\hat\varphi_q}{|q|}
|
||||
\end{equation}
|
||||
provided
|
||||
\begin{equation}
|
||||
N_i>4K_i.
|
||||
\end{equation}
|
||||
Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q\in\mathcal K$, then $|p_i+q_i|\leqslant2K_i$. Therefore,
|
||||
\begin{equation}
|
||||
T(\hat\varphi,k)
|
||||
=
|
||||
\frac1{N_1N_2}
|
||||
\mathcal F^*\left(
|
||||
\mathcal F(|p|^{-1}\hat\varphi_p)(n)
|
||||
\mathcal F((|q|^{-1}(q\cdot k^\perp)(k\cdot q)\hat\varphi_q)_q)(n)
|
||||
\right)(k)
|
||||
\end{equation}
|
||||
which we expand
|
||||
\begin{equation}
|
||||
T(\hat\varphi,k)
|
||||
=
|
||||
\textstyle
|
||||
\frac{k_x^2-k_y^2}{N_1N_2}
|
||||
\mathcal F^*\left(
|
||||
\mathcal F\left(\frac{\hat\varphi_p}{|p|}\right)(n)
|
||||
\mathcal F\left(\frac{q_xq_y}{|q|}\hat\varphi_q\right)(n)
|
||||
\right)(k)
|
||||
-
|
||||
\frac{k_xk_y}{N_1N_2}
|
||||
\mathcal F^*\left(
|
||||
\mathcal F\left(\frac{\hat\varphi_p}{|p|}\right)(n)
|
||||
\mathcal F\left(\frac{q_x^2-q_y^2}{|q|}\hat\varphi_q\right)(n)
|
||||
\right)(k)
|
||||
\end{equation}
|
||||
|
||||
|
||||
\vfill
|
||||
\eject
|
||||
|
||||
\begin{thebibliography}{WWW99}
|
||||
\small
|
||||
\IfFileExists{bibliography/bibliography.tex}{\input bibliography/bibliography.tex}{}
|
||||
\end{thebibliography}
|
||||
|
||||
|
||||
\end{document}
|
||||
282
src/main.c
Normal file
282
src/main.c
Normal file
@ -0,0 +1,282 @@
|
||||
#define VERSION "0.0"
|
||||
|
||||
#include <math.h>
|
||||
#include <complex.h>
|
||||
#include <fftw3.h>
|
||||
#include <string.h>
|
||||
#include <stdlib.h>
|
||||
#include "navier-stokes.h"
|
||||
|
||||
// usage message
|
||||
int print_usage();
|
||||
// read command line arguments
|
||||
int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nsteps, unsigned int* computation_nr);
|
||||
|
||||
// compute enstrophy as a function of time in the I-NS equation
|
||||
int enstrophy(ns_params params, unsigned int Nsteps);
|
||||
|
||||
|
||||
#define COMPUTATION_ENSTROPHY 1
|
||||
int main (int argc, const char* argv[]){
|
||||
ns_params params;
|
||||
unsigned int nsteps;
|
||||
int ret;
|
||||
unsigned int computation_nr;
|
||||
|
||||
// default computation: phase diagram
|
||||
computation_nr=COMPUTATION_ENSTROPHY;
|
||||
|
||||
// read command line arguments
|
||||
ret=read_args(argc, argv, ¶ms, &nsteps, &computation_nr);
|
||||
if(ret<0){
|
||||
return(-1);
|
||||
}
|
||||
if(ret>0){
|
||||
return(0);
|
||||
}
|
||||
|
||||
// enstrophy
|
||||
if(computation_nr==COMPUTATION_ENSTROPHY){
|
||||
enstrophy(params, nsteps);
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// usage message
|
||||
int print_usage(){
|
||||
fprintf(stderr, "usage:\n nstrophy enstrophy [-h timestep] [-K modes] [-v] [-N nsteps]\n\n nstrophy -V [-v]\n\n");
|
||||
return(0);
|
||||
}
|
||||
|
||||
// read command line arguments
|
||||
#define CP_FLAG_TIMESTEP 1
|
||||
#define CP_FLAG_NSTEPS 2
|
||||
#define CP_FLAG_MODES 2
|
||||
#define CP_FLAG_NU 3
|
||||
int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nsteps, unsigned int* computation_nr){
|
||||
int i;
|
||||
int ret;
|
||||
// temporary int
|
||||
int tmp_int;
|
||||
// temporary unsigned int
|
||||
unsigned int tmp_uint;
|
||||
// temporary double
|
||||
double tmp_double;
|
||||
// pointers
|
||||
char* ptr;
|
||||
// flag that indicates what argument is being read
|
||||
int flag=0;
|
||||
// print version and exit
|
||||
char Vflag=0;
|
||||
|
||||
// defaults
|
||||
/*
|
||||
params->h=6.103515625e-05;
|
||||
params->K=16;
|
||||
*nsteps=16777216;
|
||||
params->nu=4.9632717887631524e-05;
|
||||
*/
|
||||
params->h=1e-5;
|
||||
params->K=16;
|
||||
*nsteps=10000000;
|
||||
params->nu=1e-4;
|
||||
|
||||
// loop over arguments
|
||||
for(i=1;i<argc;i++){
|
||||
// flag
|
||||
if(argv[i][0]=='-'){
|
||||
for(ptr=((char*)argv[i])+1;*ptr!='\0';ptr++){
|
||||
switch(*ptr){
|
||||
// timestep
|
||||
case 'h':
|
||||
flag=CP_FLAG_TIMESTEP;
|
||||
break;
|
||||
// nsteps
|
||||
case 'N':
|
||||
flag=CP_FLAG_NSTEPS;
|
||||
break;
|
||||
// modes
|
||||
case 'K':
|
||||
flag=CP_FLAG_MODES;
|
||||
break;
|
||||
// friction
|
||||
case 'n':
|
||||
flag=CP_FLAG_NU;
|
||||
break;
|
||||
// print version
|
||||
case 'V':
|
||||
Vflag=1;
|
||||
break;
|
||||
default:
|
||||
fprintf(stderr, "unrecognized option '-%c'\n", *ptr);
|
||||
print_usage();
|
||||
return(-1);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
// timestep
|
||||
else if(flag==CP_FLAG_TIMESTEP){
|
||||
ret=sscanf(argv[i],"%lf",&tmp_double);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: '-h' should be followed by a double\n got '%s'\n",argv[i]);
|
||||
return(-1);
|
||||
}
|
||||
params->h=tmp_double;
|
||||
flag=0;
|
||||
}
|
||||
// nsteps
|
||||
else if(flag==CP_FLAG_NSTEPS){
|
||||
ret=sscanf(argv[i],"%u",&tmp_uint);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: '-N' should be followed by an unsigned int\n got '%s'\n",argv[i]);
|
||||
return(-1);
|
||||
}
|
||||
*nsteps=tmp_uint;
|
||||
flag=0;
|
||||
}
|
||||
// nsteps
|
||||
else if(flag==CP_FLAG_MODES){
|
||||
ret=sscanf(argv[i],"%d",&tmp_int);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: '-K' should be followed by an int\n got '%s'\n",argv[i]);
|
||||
return(-1);
|
||||
}
|
||||
params->K=tmp_uint;
|
||||
flag=0;
|
||||
}
|
||||
// friction
|
||||
else if(flag==CP_FLAG_TIMESTEP){
|
||||
ret=sscanf(argv[i],"%lf",&tmp_double);
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: '-n' should be followed by a double\n got '%s'\n",argv[i]);
|
||||
return(-1);
|
||||
}
|
||||
params->nu=tmp_double;
|
||||
flag=0;
|
||||
}
|
||||
// computation to run
|
||||
else{
|
||||
if(strcmp(argv[i], "enstrophy")==0){
|
||||
*computation_nr=COMPUTATION_ENSTROPHY;
|
||||
}
|
||||
else{
|
||||
fprintf(stderr, "error: unrecognized computation: '%s'\n",argv[i]);
|
||||
print_usage();
|
||||
return(-1);
|
||||
}
|
||||
flag=0;
|
||||
}
|
||||
}
|
||||
|
||||
// print version and exit
|
||||
if(Vflag==1){
|
||||
printf("nstrophy " VERSION "\n");
|
||||
return(1);
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// compute enstrophy as a function of time in the I-NS equation
|
||||
int enstrophy(ns_params params, unsigned int Nsteps){
|
||||
_Complex double* u;
|
||||
_Complex double* tmp1;
|
||||
_Complex double* tmp2;
|
||||
_Complex double* tmp3;
|
||||
_Complex double alpha;
|
||||
_Complex double avg;
|
||||
unsigned int t;
|
||||
int kx,ky;
|
||||
fft_vects fft_vects;
|
||||
|
||||
// sizes
|
||||
params.S=2*params.K+1;
|
||||
params.N=4*params.K+1;
|
||||
|
||||
// velocity field
|
||||
u=calloc(sizeof(_Complex double),params.S*params.S);
|
||||
params.g=calloc(sizeof(_Complex double),params.S*params.S);
|
||||
// allocate tmp vectors for computation
|
||||
tmp1=calloc(sizeof(_Complex double),params.S*params.S);
|
||||
tmp2=calloc(sizeof(_Complex double),params.S*params.S);
|
||||
tmp3=calloc(sizeof(_Complex double),params.S*params.S);
|
||||
|
||||
// initial value
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
//u[KLOOKUP(kx,ky,params.S)]=kx*kx*ky*ky*exp(-(kx*kx+ky*ky));
|
||||
if((kx==1 && ky==0) || (kx==-1 && ky==0)){
|
||||
u[KLOOKUP(kx,ky,params.S)]=1;
|
||||
}
|
||||
else{
|
||||
u[KLOOKUP(kx,ky,params.S)]=0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// driving force
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
//params.g[KLOOKUP(kx,ky,params.S)]=sqrt(kx*kx*ky*ky)*exp(-(kx*kx+ky*ky));
|
||||
if((kx==2 && ky==-1) || (kx==-2 && ky==1)){
|
||||
params.g[KLOOKUP(kx,ky,params.S)]=1;
|
||||
}
|
||||
else{
|
||||
params.g[KLOOKUP(kx,ky,params.S)]=0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// prepare vectors for fft
|
||||
fft_vects.fft1=fftw_malloc(sizeof(fftw_complex)*params.N*params.N);
|
||||
fft_vects.fft1_plan=fftw_plan_dft_2d((int)params.N,(int)params.N, fft_vects.fft1, fft_vects.fft1, FFTW_FORWARD, FFTW_MEASURE);
|
||||
fft_vects.fft2=fftw_malloc(sizeof(fftw_complex)*params.N*params.N);
|
||||
fft_vects.fft2_plan=fftw_plan_dft_2d((int)params.N,(int)params.N, fft_vects.fft2, fft_vects.fft2, FFTW_FORWARD, FFTW_MEASURE);
|
||||
fft_vects.invfft=fftw_malloc(sizeof(fftw_complex)*params.N*params.N);
|
||||
fft_vects.invfft_plan=fftw_plan_dft_2d((int)params.N,(int)params.N, fft_vects.invfft, fft_vects.invfft, FFTW_BACKWARD, FFTW_MEASURE);
|
||||
|
||||
// init running average
|
||||
avg=0;
|
||||
|
||||
// iterate
|
||||
for(t=0;t<Nsteps;t++){
|
||||
ins_step(u, params, fft_vects, tmp1, tmp2, tmp3);
|
||||
alpha=compute_alpha(u, params);
|
||||
|
||||
// to avoid errors building up in imaginary part
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
u[KLOOKUP(kx,ky,params.S)]=__real__ u[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
|
||||
// running average
|
||||
if(t>0){
|
||||
avg=avg-(avg-alpha)/t;
|
||||
}
|
||||
|
||||
if(t>0 && t%1000==0){
|
||||
fprintf(stderr,"%8d % .8e % .8e % .8e % .8e\n",t, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
|
||||
printf("%8d % .8e % .8e % .8e % .8e\n",t, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
|
||||
}
|
||||
}
|
||||
|
||||
// free memory
|
||||
fftw_destroy_plan(fft_vects.fft1_plan);
|
||||
fftw_destroy_plan(fft_vects.fft2_plan);
|
||||
fftw_destroy_plan(fft_vects.invfft_plan);
|
||||
fftw_free(fft_vects.fft1);
|
||||
fftw_free(fft_vects.fft2);
|
||||
fftw_free(fft_vects.invfft);
|
||||
|
||||
free(tmp3);
|
||||
free(tmp2);
|
||||
free(tmp1);
|
||||
free(params.g);
|
||||
free(u);
|
||||
|
||||
return(0);
|
||||
}
|
||||
299
src/navier-stokes.c
Normal file
299
src/navier-stokes.c
Normal file
@ -0,0 +1,299 @@
|
||||
#include "navier-stokes.h"
|
||||
#include <math.h>
|
||||
|
||||
#define M_PI 3.14159265358979323846
|
||||
|
||||
#define CHK 1
|
||||
|
||||
// next time step for Irreversible Navier-Stokes equation
|
||||
int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3){
|
||||
int kx,ky;
|
||||
|
||||
// k1
|
||||
ins_rhs(tmp1, u, params, vects);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp3[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/6*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
|
||||
// u+h*k1/2
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/2*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
// k2
|
||||
ins_rhs(tmp1, tmp2, params, vects);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp3[KLOOKUP(kx,ky,params.S)]+=params.h/3*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
|
||||
// u+h*k2/2
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h/2*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
// k3
|
||||
ins_rhs(tmp1, tmp2, params, vects);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp3[KLOOKUP(kx,ky,params.S)]+=params.h/3*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
|
||||
// u+h*k3
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
tmp2[KLOOKUP(kx,ky,params.S)]=u[KLOOKUP(kx,ky,params.S)]+params.h*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
// k4
|
||||
ins_rhs(tmp1, tmp2, params, vects);
|
||||
// add to output
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
u[KLOOKUP(kx,ky,params.S)]=tmp3[KLOOKUP(kx,ky,params.S)]+params.h/6*tmp1[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// right side of Irreversible Navier-Stokes equation
|
||||
int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vects vects){
|
||||
int kx,ky;
|
||||
|
||||
#if CHK==0
|
||||
// F(u/|p|)*F(q1*q2*u/|q|)
|
||||
// init to 0
|
||||
for(kx=0; kx<params.N*params.N; kx++){
|
||||
vects.fft1[kx]=0;
|
||||
vects.fft2[kx]=0;
|
||||
vects.invfft[kx]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
vects.fft1[KLOOKUP(kx,ky,params.N)]=u[KLOOKUP(kx,ky,params.S)]/sqrt(kx*kx+ky*ky);
|
||||
vects.fft2[KLOOKUP(kx,ky,params.N)]=kx*ky*u[KLOOKUP(kx,ky,params.S)]/sqrt(kx*kx+ky*ky);
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(vects.fft1_plan);
|
||||
fftw_execute(vects.fft2_plan);
|
||||
// write to invfft
|
||||
for(kx=-2*params.K;kx<=2*params.K;kx++){
|
||||
for(ky=-2*params.K;ky<=2*params.K;ky++){
|
||||
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
|
||||
}
|
||||
}
|
||||
// inverse fft
|
||||
fftw_execute(vects.invfft_plan);
|
||||
|
||||
// write out
|
||||
for(kx=0; kx<params.S*params.S; kx++){
|
||||
out[kx]=0;
|
||||
}
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
out[KLOOKUP(kx,ky,params.S)]=-4*M_PI*M_PI*params.nu*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]+params.g[KLOOKUP(kx,ky,params.S)]+4*M_PI*M_PI/sqrt(kx*kx+ky*ky)*vects.invfft[KLOOKUP(kx,ky,params.N)]*(kx*kx-ky*ky)/params.N/params.N;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// F(u/|p|)*F((q1*q1-q2*q2)*u/|q|)
|
||||
// init to 0
|
||||
for(kx=0; kx<params.N*params.N; kx++){
|
||||
vects.fft2[kx]=0;
|
||||
vects.invfft[kx]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
vects.fft2[KLOOKUP(kx,ky,params.N)]=(kx*kx-ky*ky)*u[KLOOKUP(kx,ky,params.S)]/sqrt(kx*kx+ky*ky);
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(vects.fft2_plan);
|
||||
// write to invfft
|
||||
for(kx=-2*params.K;kx<=2*params.K;kx++){
|
||||
for(ky=-2*params.K;ky<=2*params.K;ky++){
|
||||
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
|
||||
}
|
||||
}
|
||||
// inverse fft
|
||||
fftw_execute(vects.invfft_plan);
|
||||
|
||||
// write out
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
out[KLOOKUP(kx,ky,params.S)]=out[KLOOKUP(kx,ky,params.S)]-4*M_PI*M_PI/sqrt(kx*kx+ky*ky)*vects.invfft[KLOOKUP(kx,ky,params.N)]*(kx*ky)/params.N/params.N;
|
||||
}
|
||||
}
|
||||
}
|
||||
#elif CHK == 1
|
||||
// F(-p2/|p|*u)*F(q1*|q|*u)
|
||||
// init to 0
|
||||
for(kx=0; kx<params.N*params.N; kx++){
|
||||
vects.fft1[kx]=0;
|
||||
vects.fft2[kx]=0;
|
||||
vects.invfft[kx]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
vects.fft1[KLOOKUP(kx,ky,params.N)]=-kx/sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
|
||||
vects.fft2[KLOOKUP(kx,ky,params.N)]=kx*sqrt(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(vects.fft1_plan);
|
||||
fftw_execute(vects.fft2_plan);
|
||||
// write to invfft
|
||||
for(kx=-2*params.K;kx<=2*params.K;kx++){
|
||||
for(ky=-2*params.K;ky<=2*params.K;ky++){
|
||||
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)] - vects.fft1[KLOOKUP(ky,kx,params.N)]*vects.fft2[KLOOKUP(ky,kx,params.N)];
|
||||
}
|
||||
}
|
||||
|
||||
// inverse fft
|
||||
fftw_execute(vects.invfft_plan);
|
||||
|
||||
|
||||
// write out
|
||||
for(kx=0; kx<params.S*params.S; kx++){
|
||||
out[kx]=0;
|
||||
}
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
out[KLOOKUP(kx,ky,params.S)]=-4*M_PI*M_PI*params.nu/params.S*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]+params.g[KLOOKUP(kx,ky,params.S)]+2*M_PI/sqrt(kx*kx+ky*ky)/params.S*vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#elif CHK==2
|
||||
// F(u)*F(q1*u)
|
||||
// init to 0
|
||||
for(kx=0; kx<params.N*params.N; kx++){
|
||||
vects.fft1[kx]=0;
|
||||
vects.fft2[kx]=0;
|
||||
vects.invfft[kx]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
// u_k
|
||||
vects.fft1[KLOOKUP(kx,ky,params.N)]=u[KLOOKUP(kx,ky,params.S)];
|
||||
// 2i\pi k_x u_k
|
||||
vects.fft2[KLOOKUP(kx,ky,params.N)]=2*M_PI*I*kx*u[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(vects.fft1_plan);
|
||||
fftw_execute(vects.fft2_plan);
|
||||
// write to invfft
|
||||
for(kx=-2*params.K;kx<=2*params.K;kx++){
|
||||
for(ky=-2*params.K;ky<=2*params.K;ky++){
|
||||
vects.invfft[KLOOKUP(kx,ky,params.N)]=vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
|
||||
}
|
||||
}
|
||||
|
||||
// F(p1/p2*u)*F(q2*u)
|
||||
// init to 0
|
||||
for(kx=0; kx<params.N*params.N; kx++){
|
||||
vects.fft1[kx]=0;
|
||||
vects.fft2[kx]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
// k_x/k_y u_k
|
||||
if(ky!=0){
|
||||
vects.fft1[KLOOKUP(kx,ky,params.N)]=kx/ky*u[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
// 2i\pi k_y u_k
|
||||
vects.fft2[KLOOKUP(kx,ky,params.N)]=2*M_PI*I*ky*u[KLOOKUP(kx,ky,params.S)];
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(vects.fft1_plan);
|
||||
fftw_execute(vects.fft2_plan);
|
||||
// write to invfft
|
||||
for(kx=-2*params.K;kx<=2*params.K;kx++){
|
||||
for(ky=-2*params.K;ky<=2*params.K;ky++){
|
||||
vects.invfft[KLOOKUP(kx,ky,params.N)]+=-vects.fft1[KLOOKUP(kx,ky,params.N)]*vects.fft2[KLOOKUP(kx,ky,params.N)];
|
||||
}
|
||||
}
|
||||
|
||||
// inverse fft
|
||||
fftw_execute(vects.invfft_plan);
|
||||
|
||||
/*
|
||||
// check: convolution instead of fft
|
||||
for(kx=0; kx<params.S*params.S; kx++){
|
||||
out[kx]=0;
|
||||
}
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
for(px=-params.K;px<=params.K;px++){
|
||||
for(py=-params.K;py<=params.K;py++){
|
||||
if(kx-px<=params.K && kx-px>=-params.K && ky-py<=params.K && ky-py>=-params.K){
|
||||
out[KLOOKUP(kx,ky,params.S)]+=2*M_PI*I*(u[KLOOKUP(px,py,params.S)]*(kx-px)*u[KLOOKUP(kx-px,ky-py,params.S)]-(py==0?0:px/py*u[KLOOKUP(px,py,params.S)]*(ky-py)*u[KLOOKUP(kx-px,ky-py,params.S)]));
|
||||
}
|
||||
}
|
||||
}
|
||||
dd=(__real__ vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N-__real__ out[KLOOKUP(kx,ky,params.S)])*(__real__ vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N-__real__ out[KLOOKUP(kx,ky,params.S)])+(__imag__ vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N-__imag__ out[KLOOKUP(kx,ky,params.S)])*(__imag__ vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N-__imag__ out[KLOOKUP(kx,ky,params.S)]);
|
||||
if(dd>1e-25){
|
||||
printf("%d %d % .8e\n",kx,ky, dd);
|
||||
}
|
||||
}
|
||||
}
|
||||
*/
|
||||
|
||||
|
||||
// write out
|
||||
for(kx=0; kx<params.S*params.S; kx++){
|
||||
out[kx]=0;
|
||||
}
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
out[KLOOKUP(kx,ky,params.S)]=-4*M_PI*M_PI*params.nu*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]+params.g[KLOOKUP(kx,ky,params.S)]+vects.invfft[KLOOKUP(kx,ky,params.N)]/params.N/params.N;
|
||||
}
|
||||
}
|
||||
|
||||
#endif
|
||||
return(0);
|
||||
}
|
||||
|
||||
|
||||
// compute alpha
|
||||
_Complex double compute_alpha(_Complex double* u, ns_params params){
|
||||
_Complex double num=0;
|
||||
_Complex double denom=0;
|
||||
int kx,ky;
|
||||
|
||||
for(kx=-params.K;kx<=params.K;kx++){
|
||||
for(ky=-params.K;ky<=params.K;ky++){
|
||||
denom+=(kx*kx+ky*ky)*(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]*conj(u[KLOOKUP(kx,ky,params.S)])*(1+(ky!=0?kx*kx/ky/ky:0));
|
||||
num+=(kx*kx+ky*ky)*u[KLOOKUP(kx,ky,params.S)]*conj(params.g[KLOOKUP(kx,ky,params.S)])*(1+(ky!=0?kx*kx/ky/ky:0));
|
||||
}
|
||||
}
|
||||
|
||||
return(num/denom);
|
||||
}
|
||||
48
src/navier-stokes.h
Normal file
48
src/navier-stokes.h
Normal file
@ -0,0 +1,48 @@
|
||||
#ifndef NAVIERSTOKES_H
|
||||
#define NAVIERSTOKES_H
|
||||
|
||||
#include <complex.h>
|
||||
#include <fftw3.h>
|
||||
|
||||
// to extract elements from array of size S representing a function of momentum, use
|
||||
// array[KEXTRACT(kx,ky,size)]
|
||||
#define KLOOKUP(X,Y,S) (X>=0?X:S+X)*S+(Y>=0?Y:S+Y)
|
||||
|
||||
|
||||
// parameters for the NS equation
|
||||
typedef struct ns_params {
|
||||
// number of modes
|
||||
int K;
|
||||
// 2*K+1
|
||||
int S;
|
||||
// 4*K+1
|
||||
int N;
|
||||
// forcing term
|
||||
_Complex double* g;
|
||||
// time step
|
||||
double h;
|
||||
// friction
|
||||
double nu;
|
||||
} ns_params;
|
||||
|
||||
// arrays on which the ffts are performed
|
||||
typedef struct fft_vects {
|
||||
fftw_complex* fft1;
|
||||
fftw_complex* fft2;
|
||||
fftw_complex* invfft;
|
||||
fftw_plan fft1_plan;
|
||||
fftw_plan fft2_plan;
|
||||
fftw_plan invfft_plan;
|
||||
} fft_vects;
|
||||
|
||||
// next time step for Irreversible Navier-Stokes equation
|
||||
int ins_step(_Complex double* u, ns_params params, fft_vects vects, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3);
|
||||
|
||||
// right side of Irreversible Navier-Stokes equation
|
||||
int ins_rhs(_Complex double* out, _Complex double* u, ns_params params, fft_vects vects);
|
||||
|
||||
// compute alpha
|
||||
_Complex double compute_alpha(_Complex double* u, ns_params params);
|
||||
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user