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Corrections in doc

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This commit is contained in:
Ian Jauslin 2022-05-12 09:32:58 +02:00
parent cbf2b9854a
commit 35d91830a2
2 changed files with 9 additions and 6 deletions
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7
docs/nstrophy_doc/nstrophy_doc.tex
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@ -50,7 +50,7 @@ in terms of which, multiplying both sides of the equation by $\frac{k^\perp}{|k|
\partial_t\hat \varphi_k= \partial_t\hat \varphi_k=
-4\pi^2\nu k^2\hat \varphi_k+\frac{k^\perp}{2i\pi|k|}\cdot\hat g_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}} +\frac{4\pi^2}{|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 \frac{(q\cdot p^\perp)(k^\perp\cdot q^\perp)}{|q||p|}\hat\varphi_p\hat\varphi_q
. .
\label{ins_k} \label{ins_k}
\end{equation} \end{equation}
@ -88,7 +88,7 @@ using a fast Fourier transform, defined as
\end{equation} \end{equation}
where where
\begin{equation} \begin{equation}
\mathcal N:=\{(n_1,n_2),\ 0\leqslant n_1\leqslant N_1,\ 0\leqslant n_2\leqslant N_2\} \mathcal N:=\{(n_1,n_2),\ 0\leqslant n_1< N_1,\ 0\leqslant n_2< N_2\}
\end{equation} \end{equation}
for some fixed $N_1,N_2$. The transform is inverted by for some fixed $N_1,N_2$. The transform is inverted by
\begin{equation} \begin{equation}
@ -110,7 +110,8 @@ provided
\begin{equation} \begin{equation}
N_i>4K_i. N_i>4K_i.
\end{equation} \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, 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} \begin{equation}
T(\hat\varphi,k) T(\hat\varphi,k)
= =

8
src/main.c
View File

@ -77,10 +77,12 @@ int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nst
*nsteps=10000000; *nsteps=10000000;
params->nu=1./1024/(2*params->K+1); params->nu=1./1024/(2*params->K+1);
*/ */
params->K=3; params->K=16;
params->h=0.0001220703125; params->h=0.0001220703125;
params->h=0.001953125;
*nsteps=10000000; *nsteps=10000000;
params->nu=0.00048828125; //params->nu=0.00048828125;
params->nu=0.0078125;
// loop over arguments // loop over arguments
for(i=1;i<argc;i++){ for(i=1;i<argc;i++){
@ -291,7 +293,7 @@ int enstrophy(ns_params params, unsigned int Nsteps){
avg=avg-(avg-alpha)/t; avg=avg-(avg-alpha)/t;
} }
if(t>0 && t%8192==0){ if(t>0 && t%1000==0){
fprintf(stderr,"%8d % .8e % .8e % .8e % .8e\n",t, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha); 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); printf("%8d % .8e % .8e % .8e % .8e\n",t, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
} }