src/examples/isotropic.c
Forced isotropic turbulence in a triply-periodic box
We compute the evolution of forced isotropic turbulence (see Rosales & Meneveau, 2005) and compare the solution to that of the hit3d pseudo-spectral code. The initial condition is an unstable solution to the incompressible Euler equations. Numerical noise in the solution eventually leads to the destabilisation of the base solution into a fully turbulent flow where turbulent dissipation balances the linear input of energy.
#include "grid/multigrid3D.h"
#include "navier-stokes/centered.h"We use the \lambda_2 criterion and Basilisk View for visualisation of vortices.
We monitor performance statistics and control the maximum runtime.
#include "navier-stokes/perfs.h"
#include "maxruntime.h"
const double MU = 0.01;We need to store the variable forcing term.
face vector av[];The code takes the level of refinement as optional command-line argument (as well as an optional maximum runtime).
int maxlevel = 7;
int main (int argc, char * argv[])
{
maxruntime (&argc, argv);
if (argc > 1)
maxlevel = atoi(argv[1]);The domain is (2\pi)^3 and triply-periodic.
L0 = 2.*pi [1];
foreach_dimension()
periodic (right);The viscosity is constant. The acceleration is defined below. The level of refinement is maxlevel.
mu[] = {MU,MU,MU};
a = av;
N = 1 << maxlevel;
run();
}Initial conditions
The initial condition is “ABC” flow. This is a laminar base flow that is easy to implement in both Basilisk and a spectral code.
event init (i = 0) {
double u0 = 1., k = 1.;
if (!restore (file = "restart"))
foreach() {
u.x[] = u0*(cos(k*y) + sin(k*z));
u.y[] = u0*(sin(k*x) + cos(k*z));
u.z[] = u0*(cos(k*x) + sin(k*y));
}
}Linear forcing term
We compute the average velocity and add the corresponding linear forcing term.
event acceleration (i++) {
coord ubar;
foreach_dimension() {
stats s = statsf(u.x);
ubar.x = s.sum/s.volume;
}
double a = 0.1;
foreach_face()
av.x[] += a*((u.x[] + u.x[-1])/2. - ubar.x);
}Outputs
We log the evolution of viscous dissipation, kinetic energy, and microscale Reynolds number.
event logfile (i++; t <= 300) {
coord ubar;
foreach_dimension() {
stats s = statsf(u.x);
ubar.x = s.sum/s.volume;
}
double ke = 0., vd = 0., vol = 0.;
foreach(reduction(+:ke) reduction(+:vd) reduction(+:vol)) {
vol += dv();
foreach_dimension() {
// mean fluctuating kinetic energy
ke += dv()*sq(u.x[] - ubar.x);
// viscous dissipation
vd += dv()*(sq(u.x[1] - u.x[-1]) +
sq(u.x[0,1] - u.x[0,-1]) +
sq(u.x[0,0,1] - u.x[0,0,-1]))/sq(2.*Delta);
}
}
ke /= 2.*vol;
vd *= MU/vol;
if (i == 0)
fprintf (stderr, "t dissipation energy Reynolds\n");
fprintf (stderr, "%g %g %g %g\n",
t, vd, ke, 2./3.*ke/MU*sqrt(15.*MU/vd));
}We generate a movie of the vortices.
Animation of the \lambda_2 isosurface (a way to characterise vortices) and cross-sections of velocity and vorticity.
event movie (t += 0.25; t <= 150)
{
view (fov = 44, camera = "iso", ty = .2,
width = 600, height = 600, bg = {1,1,1}, samples = 4);
clear();
squares ("u.y", linear = true);
squares ("u.x", linear = true, n = {1,0,0});
scalar omega[];
vorticity (u, omega);
squares ("omega", linear = true, n = {0,1,0});
scalar l2[];
lambda2 (u, l2);
isosurface ("l2", -1);
save ("movie.mp4");
}We can optionally try adaptivity.
#if TREE
event adapt (i++) {
double uemax = 0.2*normf(u.x).avg;
adapt_wavelet ((scalar *){u}, (double[]){uemax,uemax,uemax}, maxlevel);
}
#endifRunning with MPI on occigen
On the local machine
%local qcc -source -D_MPI=1 isotropic.c
%local scp _isotropic.c occigen.cines.fr:On occigen (using 512 cores)
module purge
module load openmpi
module load intel
mpicc -Wall -O2 -std=c99 -D_XOPEN_SOURCE=700 _isotropic.c -o isotropic \
-I$HOME -L$HOME/gl -lglutils -lfb_tiny -lm
sed 's/WALLTIME/10:00/g' run.sh | sbatchNote that this assumes that the Basilisk gl libraries have been installed in $HOME/gl.
With the run.sh script
#!/bin/bash
#SBATCH -J basilisk
#SBATCH --nodes=32
#SBATCH --constraint=HSW24
#SBATCH --ntasks-per-node=16
#SBATCH --threads-per-core=1
#SBATCH --time=WALLTIME
#SBATCH --output basilisk.output
#SBATCH --exclusive
LEVEL=7
module purge
module load openmpi
module load intel
srun --mpi=pmi2 -K1 --resv-ports -n $SLURM_NTASKS \
./isotropic -m WALLTIME $LEVEL \
2> log-$LEVEL-$SLURM_NTASKS > out-$LEVEL-$SLURM_NTASKSRunning with MPI on mesu
On the local machine
%local qcc -source -D_MPI=1 isotropic.c
%local scp _isotropic.c mesu.dsi.upmc.fr:On mesu (using 512 cores)
module load mpt
mpicc -Wall -O2 -std=c99 -D_XOPEN_SOURCE=700 _isotropic.c -o isotropic \
-L$HOME/gl -lglutils -lfb_tiny -lm
sed 's/WALLTIME/10:00/g' run.sh | qsubwith the run.sh script
#!/bin/bash
#PBS -l select=22:ncpus=24:mpiprocs=24
#PBS -l walltime=WALLTIME
#PBS -N isotropic
#PBS -j oe
# load modules
module load mpt
# change to the directory where program job_script_file is located
cd $PBS_O_WORKDIR
# mpirun -np 64 !!!! does not work !!!!
NP=512
mpiexec_mpt -n $NP ./isotropic -m WALLTIME 2>> log.$NP >> out.$NPResults
The two codes agree at early time, or until the solution transitions to a turbulent state. The statistics produced by the two codes agree well after transition to turbulence.
set xlabel 'Time'
set ylabel 'Kinetic energy'
set logscale y
plot 'isotropic.occigen' u 1:3 w l t 'Basilisk (occigen)', \
'isotropic.mesu' u 1:3 w l t 'Basilisk (mesu)', \
'isotropic.hit3d' u 1:($3*3./2.) w l t 'Spectral'
Evolution of kinetic energy (script)
set ylabel 'Microscale Reynolds number'
plot 'isotropic.occigen' u 1:4 w l t 'Basilisk (occigen)', \
'isotropic.mesu' u 1:4 w l t 'Basilisk (mesu)', \
'isotropic.hit3d' u 1:4 w l t 'Spectral'
Evolution of microscale Reynolds number (script)
set ylabel 'Dissipation function'
plot 'isotropic.occigen' u 1:2 w l t 'Basilisk (occigen)', \
'isotropic.mesu' u 1:2 w l t 'Basilisk (mesu)', \
'isotropic.hit3d' u 1:2 w l t 'Spectral'
Evolution of dissipation (script)
The computational speed is respectable (for a relatively small 1283 problem on 512 cores). Note that these were obtained when switching off movie outputs.
set ylabel 'Speed'
unset logscale
plot 'isotropic.occigen' u 1:($7/512) w l t 'occigen', \
'isotropic.mesu' u 1:($7/512) w l t 'mesu'
Computational speed in points.timesteps/sec/core (script)
Scalability on irene
Irene is the supercomputer at CEA.
On the local machine
%local qcc -source -D_MPI=1 isotropic.c
%local scp _isotropic.c irene.ccc.cea.fr:On irene
mpicc -Wall -O2 -std=c99 -D_XOPEN_SOURCE=700 -xCORE-AVX512 \
_isotropic.c -o isotropic \
-L$HOME/gl -lglutils -lfb_tiny -lm
sed -e 's/WALLTIME/600/g' -e 's/LEVEL/7/g' run.sh | ccc_msub -n 512with the run.sh script
#!/bin/bash
#MSUB -r isotropic
#MSUB -T WALLTIME
#MSUB -o basilisk_%I.out
#MSUB -e basilisk_%I.log
#MSUB -q skylake
#MSUB -A gen7760
#MSUB -m scratch
set -x
cd ${BRIDGE_MSUB_PWD}
ccc_mprun -n ${BRIDGE_MSUB_NPROC} ./isotropic -m WALLTIME LEVEL \
2> log-${BRIDGE_MSUB_NPROC} > out-${BRIDGE_MSUB_NPROC}set xlabel '# of cores'
set ylabel 'Speed (points x timestep/sec/core)'
set logscale x
plot '-' w lp t ''
8 366497
64 273009
512 196904
4096 167429
e
Weak scaling on Irene (163 per core) (script)
set xlabel '# of cores'
set ylabel 'Speed (points x timestep/sec/core)'
set logscale x
plot '-' w lp t ''
8 281250
64 189218
512 165312
4096 156683
e
Weak scaling on Irene (323 per core) (script)
