License

LICENSE

@@ -0,0 +1,202 @@
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Makefile

@@ -1,3 +1,17 @@
+# Copyright 2017-2023 Ian Jauslin
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
 PROJECTNAME=nstrophy
 VERSION=0.0
 

README.md

@@ -0,0 +1,112 @@
+Nstrophy is a tool to solve the two-dimensional Navier-Stokes equation as well
+as Gallavotti's reversible Navier-Stokes equation and compare them.
+
+**Nstrophy is under active development**
+
+# Building
+
+Compile Nstrophy with
+```bash
+make
+```
+which will place a binary at `build/nstrophy`.
+
+The syntax for the execution of Nstrophy is
+```bash
+./build/nstrophy [-p parameters] [-s savefile] <command>
+```
+
+Nstrophy is written in C. The Makefile uses the GNU C Compiler.
+
+Nstrophy depends on `fftw`: [https://fftw.org]
+
+
+# Commands
+
+The available commands are
+
+* `enstrophy`: to compute the enstrophy, the parameter alpha and
+  alpha times the enstrophy. This command prints
+  `step_index time average_alpha average_enstrophy average_alphaxenstrophy alpha enstrophy alphaxenstrophy`
+  where the averages are running averages over `print_freq` steps.
+
+* `uk`: to compute the Fourier transform of the solution.
+
+* `quiet`: does not print anything, useful for debugging.
+
+
+# Parameters
+
+The parameters can be specified using the `-p` flag. The parameter string
+should be a `;` sperated list of `key=value` pairs. The possible keys are
+
+* `equation`: either `irreverisible` (default) or `reversible`.
+
+* `K` (int, default 16): cutoff in momentum space: -K<=k_i<=K
+
+* `K1` (int, default `K`): cutoff in momentum space for the x component:
+  -K<=k_x<=K
+
+* `K2` (int, default `K`): cutoff in momentum space for the y component:
+  -K<=k_y<=K
+
+* `N` (int, default smallest power of 2 that is larger than 3`K`): size of fft
+  vectors: must be at least 3 times `K` to avoid aliasing.
+
+* `N1` (int, default `N`): same as `N` but only for x component.
+
+* `N2` (int, default `N`): same as `N` but only for y component.
+
+* `nsteps` (long int, default 10000000): number of steps in the computation.
+  Set to 0 to keep on going forever.
+
+* `nu` (double, default 0.00048828125): viscosity.
+
+* `delta` (double, default 0.0001220703125): step size.
+
+* `L` (double, default 2pi): size of box.
+
+* `print_freq` (long int, default 1000): only print every `print_freq` steps.
+
+* `starting_time` (long int, default 0): start the computation at this step.
+
+* `driving`: either `zero` for no driving, `test` (default) for a testing
+  driving force or `file:<filename>` or `file_txt:<filename>` to read the
+  driving force from a file. When using `file:<filename>` the file should be
+  binary, whereas with `file_txt:<filename>` it should be plaintext. The binary
+  file format is `(double)(double)` for each entry of the driving force,
+  excluding kx<0 and kx=0&&ky<=0. The plaintext file format is
+  `kx ky real_part imag_part`.
+
+* `init`: either `random` for a random initialization, `gaussian` (default) for
+  a Gaussian initial condition or `file:<filename>` or `file_txt:<filename>` to
+  read the driving force from a file. When using `file:<filename>` the file
+  should be binary, whereas with `file_txt:<filename>` it should be plaintext.
+  The binary file format is `(double)(double)` for each entry of the driving
+  force, excluding kx<0 and kx=0&&ky<=0. The plaintext file format is
+  `kx ky real_part imag_part`.
+
+* `init_en` (double, default 1.54511597324389e+02): initial value of the energy if
+  `equation=irreversible` or of the enstrophy if `equation=reversible`.
+
+* `random_seed` (int, default ): seed for random initialization.
+
+* `algorithm`: either `RK4` for Runge-Kutta 4, or `RK2` for Runge-Kutta 2.
+
+
+# Interrupting/resuming the computation
+
+The computation can be interrupted by sending Nstrophy the `SIGINT` signal
+(e.g. by pressing `Ctrl-C`.) When Nstrophy receives the `SIGINT` signal, it
+finishes its current step and writes the value of uk, either to `savefile` if
+such a file was specified on the command line (using the `-s` flag), or to
+`stderr`. In addition, when a `savefile` is specified it writes the command
+that needs to be used to resume the computation (which essentially just sets
+the appropriate `starting_time` and `init:file:<savefile>` parameters. The data
+written to the `savefile` is binary.
+
+
+# License
+Nstrophy is released under the Apache 2.0 license.
+
+Copyright 2017-2023 Ian Jauslin

docs/nstrophy_doc.tex

@@ -1,3 +1,17 @@
+% Copyright 2017-2023 Ian Jauslin
+% 
+% Licensed under the Apache License, Version 2.0 (the "License");
+% you may not use this file except in compliance with the License.
+% You may obtain a copy of the License at
+% 
+%     http://www.apache.org/licenses/LICENSE-2.0
+% 
+% Unless required by applicable law or agreed to in writing, software
+% distributed under the License is distributed on an "AS IS" BASIS,
+% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+% See the License for the specific language governing permissions and
+% limitations under the License.
+
 \documentclass{ian}
 
 \usepackage{largearray}

src/constants.cpp

@@ -1,5 +1,22 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+
 #define COMMAND_UK 1
-#define COMMAND_EEA 2
+#define COMMAND_ENSTROPHY 2
 #define COMMAND_QUIET 3
 
 #define DRIVING_ZERO 1

src/driving.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #include "driving.h"
 #include "navier-stokes.h"
 #include "io.h"

src/driving.h

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #ifndef DRIVING_H
 #define DRIVING_H
 

src/init.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #include "init.h"
 #include "navier-stokes.h"
 #include "io.h"

src/init.h

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #ifndef INIT_H
 #define INIT_H
 

src/int_tools.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #include <math.h>
 #include "int_tools.h"
 

src/int_tools.h

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #ifndef INTTOOLS_H
 #define INTTOOLS_H
 

src/io.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #include <stdbool.h>
 #include <stdlib.h>
 #include <string.h>

src/io.h

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #ifndef IO_H
 #define IO_H
 

src/main.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #define VERSION "0.1"
 
 #include <math.h>
@@ -155,10 +171,10 @@ int main (
   if (command==COMMAND_UK){
     uk(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_time, nthreads, savefile);
   }
-  else if(command==COMMAND_EEA){
+  else if(command==COMMAND_ENSTROPHY){
     // register signal handler to handle aborts
     signal(SIGINT, sig_handler);
-    eea(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_time, nthreads, savefile, (char*)argv[0], param_str, savefile_str);
+    enstrophy(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, u0, g, parameters.irreversible, parameters.algorithm, parameters.print_freq, parameters.starting_time, nthreads, savefile, (char*)argv[0], param_str, savefile_str);
   }
   else if(command==COMMAND_QUIET){
     quiet(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.nsteps, parameters.nu, parameters.delta, parameters.L, parameters.starting_time, u0, g, parameters.irreversible, parameters.algorithm, nthreads, savefile);
@@ -322,8 +338,8 @@ int read_args(
       if(strcmp(argv[i], "uk")==0){
 	*command=COMMAND_UK;
       }
-      else if(strcmp(argv[i], "energy")==0){
-	*command=COMMAND_EEA;
+      else if(strcmp(argv[i], "enstrophy")==0){
+	*command=COMMAND_ENSTROPHY;
       }
       else if(strcmp(argv[i], "quiet")==0){
 	*command=COMMAND_QUIET;

src/navier-stokes.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #include "constants.cpp"
 #include "io.h"
 #include "navier-stokes.h"
@@ -84,8 +100,8 @@ int uk(
   return(0);
 }
 
-// compute energy, enstrophy, alpha as a function of time in the I-NS equation
-int eea(
+// compute enstrophy, alpha as a function of time
+int enstrophy(
   int K1,
   int K2,
   int N1,
@@ -111,8 +127,8 @@ int eea(
   _Complex double* tmp1;
   _Complex double* tmp2;
   _Complex double* tmp3;
-  double alpha, energy, enstrophy;
-  double avg_e,avg_a,avg_en;
+  double alpha, enstrophy;
+  double avg_a,avg_en,avg_en_x_a;
   // index
   uint64_t t;
   fft_vect fft1;
@@ -125,9 +141,9 @@ int eea(
 
 
   // init running average
-  avg_e=0;
   avg_a=0;
   avg_en=0;
+  avg_en_x_a=0;
 
   // special first case when starting_time is not a multiple of print_freq
   uint64_t first_box = print_freq - (starting_time % print_freq);
@@ -140,17 +156,16 @@ int eea(
       ns_step_rk4(u, K1, K2, N1, N2, nu, delta, L, g, fft1, fft2, ifft, tmp1, tmp2, tmp3, irreversible);
     }
 
-    energy=compute_energy(u, K1, K2);
     alpha=compute_alpha(u, K1, K2, g, L);
     enstrophy=compute_enstrophy(u, K1, K2, L);
 
-    avg_e=average_step(energy, avg_e, t, starting_time, print_freq, first_box);
     avg_a=average_step(alpha, avg_a, t, starting_time, print_freq, first_box);
     avg_en=average_step(enstrophy, avg_en, t, starting_time, print_freq, first_box);
+    avg_en_x_a=average_step(enstrophy*alpha, avg_en_x_a, t, starting_time, print_freq, first_box);
 
     if(t>starting_time && t%print_freq==0){
-      fprintf(stderr,"%lu % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",t,t*delta, avg_a, avg_e, avg_en, alpha, energy, enstrophy);
-      printf("%8lu % .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",t,t*delta, avg_a, avg_e, avg_en, alpha, energy, enstrophy);
+      fprintf(stderr,"%lu % .8e % .8e % .8e % .8e % .8e % .8e % .8e\n",t,t*delta, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy);
+      printf("%8lu % .15e % .15e % .15e % .15e % .15e % .15e % .15e\n",t,t*delta, avg_a, avg_en_x_a, avg_en, alpha, alpha*enstrophy, enstrophy);
     }
 
     // catch abort signal
@@ -180,7 +195,7 @@ int eea(
       fprintf(savefile," -p \"%s;starting_time=%lu;nsteps=%lu;init=file:%s\"", params, t+1, (nsteps+starting_time < t+1 ? 0 : nsteps+starting_time-t-1), savefile_string);
       free(params);
     }
-    fprintf(savefile," energy\n");
+    fprintf(savefile," enstrophy\n");
 
     // save final u to savefile
     if(savefile==stderr || savefile==stdout){

src/navier-stokes.h

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #ifndef NAVIERSTOKES_H
 #define NAVIERSTOKES_H
 
@@ -20,8 +36,8 @@ typedef struct fft_vects {
 // compute u_k
 int uk( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreadsl, FILE* savefile);
 
-// compute energy, enstrophy and alpha
-int eea( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreads, FILE* savefile, char* cmd_string, char* params_string, char* savefile_string);
+// compute enstrophy and alpha
+int enstrophy( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreads, FILE* savefile, char* cmd_string, char* params_string, char* savefile_string);
 
 // compute solution as a function of time, but do not print anything (useful for debugging)
 int quiet( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, uint64_t starting_time, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, unsigned int nthreads, FILE* savefile);

src/statistics.c

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #include "statistics.h"
 
 // run this at each step to compute the running average

src/statistics.h

@@ -1,3 +1,19 @@
+/*
+Copyright 2017-2023 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
 #ifndef STATISTICS_H
 #define STATISTICS_H