3D Navier-Stokes - Unsteady, incompressible, viscous flow around a cylinder with vortex shedding (Time-Windowed DMD)
See Unsteady, incompressible, viscous flow around a cylinder (vortex shedding) to familiarize yourself with this case.
Location: hypar/Examples/3D/NavierStokes3D/2D_Cylinder/Unsteady_Viscous_Incompressible_libROM_DMD_Train
Governing equations: 3D Navier-Stokes Equations (navierstokes3d.h)
Reduced Order Modeling: This example trains a DMD object and then predicts the solution using the DMD at the same times that the actual HyPar solution is written at.
Domain: The domain consists of a fine uniform grid around the cylinder defined by [-4,12] X [-2,2], and a stretched grid beyond this zone. Note: This is a 2D flow simulated using a 3-dimensional setup by taking the length of the domain along z to be very small and with only 3 grid points (the domain size along z must be smaller than the cylinder length).
Geometry: A cylinder of radius 1.0 centered at (0,0) (hypar/Examples/STLGeometries/cylinder.stl)
See Unsteady, incompressible, viscous flow around a cylinder (vortex shedding) for pictures show the domain and geometry.
Boundary conditions:
- xmin: Subsonic inflow _SUBSONIC_INFLOW_
- xmax: Subsonic outflow _SUBSONIC_OUTFLOW_
- ymin and ymax: Subsonic "ambivalent" _SUBSONIC_AMBIVALENT_
- zmin and zmax: Periodic _PERIODIC_ (to simulate a 2D flow in the x-y plane)
- The immersed body wall is specified as adiabatic (_IB_ADIABATIC_); (this is the default).
Reference:
- Taneda, S., Experimental Investigation of the Wakes behind Cylinders and Plates at Low Reynolds Numbers, Journal of the Physical Society of Japan, Vol. 11, 302–307, 1956.
Initial solution: \(\rho=1, u=0.1, v=w=0, p=1/\gamma\) everywhere in the domain.
Other parameters (all dimensional quantities are in SI units):
- Specific heat ratio \(\gamma = 1.4\) (NavierStokes3D::gamma)
- Freestream Mach number \(M_{\infty} = 0.1\) (NavierStokes3D::Minf)
- Prandlt number \(Pr = 0.72\) (NavierStokes3D::Pr)
- Reynolds number \(Re = \frac {\rho u L } {\mu} = 50\) (NavierStokes3D::Re) (Note: since the diameter of the cylinder is 2.0, the cylinder-diameter-based Reynolds number is \(Re_D = 2Re = 100\).
Numerical Method:
- Spatial discretization (hyperbolic): 5th order WENO (Interp1PrimFifthOrderWENO())
- Spatial discretization (parabolic) : 4th order (FirstDerivativeFourthOrderCentral()) non-conservative 2-stage (NavierStokes3DParabolicFunction())
- Time integration: RK4 (TimeRK(), _RK_44_)
Reduced Order Modeling:
- Mode: train (libROMInterface::m_mode, _ROM_MODE_TRAIN_)
- Component Mode: monolithic (libROMInterface::m_comp_mode, _ROM_COMP_MODE_MONOLITHIC_)
- Type: Dynamic Mode Decomposition (DMD) with time windowing (libROMInterface::m_rom_type)
- Latent subspace dimension: 16 (DMDROMObject::m_rdim)
- Sampling frequency: 2 (libROMInterface::m_sampling_freq)
- Number of samples per time window: 1000 (DMDROMObject::m_num_window_samples)
Input files required:
These files are all located in: hypar/Examples/3D/NavierStokes3D/2D_Cylinder/Unsteady_Viscous_Incompressible_libROM_DMD_Train/
librom.inp
begin
rdim 16
sampling_frequency 2
mode train
dmd_num_win_samples 1000
end
solver.inp
begin
ndims 3
nvars 5
size 400 96 3
iproc 8 4 1
ghost 3
n_iter 10000
time_scheme rk
time_scheme_type 44
hyp_space_scheme weno5
hyp_interp_type components
par_space_type nonconservative-2stage
par_space_scheme 4
dt 0.04
screen_op_iter 50
file_op_iter 250
ip_file_type binary
op_file_format binary
op_overwrite no
model navierstokes3d
immersed_body cylinder.stl
end
boundary.inp
6
subsonic-inflow 0 1 0 0 -9999.0 9999.0 -9999.0 9999.0
1.0 0.1 0.0 0.0
subsonic-outflow 0 -1 0 0 -9999.0 9999.0 -9999.0 9999.0
0.7142857142857143
subsonic-ambivalent 1 1 -9999.0 9999.0 0 0 -9999.0 9999.0
1.0 0.1 0.0 0.0 0.7142857142857143
subsonic-ambivalent 1 -1 -9999.0 9999.0 0 0 -9999.0 9999.0
1.0 0.1 0.0 0.0 0.7142857142857143
periodic 2 1 -9999.0 9999.0 -9999.0 9999.0 0 0
periodic 2 -1 -9999.0 9999.0 -9999.0 9999.0 0 0
physics.inp
begin
gamma 1.4
upwinding roe
Pr 0.72
Minf 0.1
Re 50
end
cylinder.stl : the filename "cylinder.stl" must match the input for immersed_body in solver.inp.
Located at hypar/Examples/STLGeometries/cylinder.stl
To generate initial.inp (initial solution), the following code will generate the domain with a clustered mesh and uniform horizontal flow. It will take time to develop the time-periodic vortex shedding flow from this initial solution. The following steps are recommended:
- Use the code below to generate a initial solution file (initial.inp) in a separate directory, and set the n_iter to 50000 in that directory. Change op_overwrite to "yes" to avoid writing too many solution files. Run HyPar.
- Use the code hypar/Extras/BinaryOPToInitialSolution.c to generate the initial solution file from the final solution of the above simulation. This code will write out a file called "solution.inp"; just rename it to "initial.inp" and place it in the directory where this simulation will be run.
- Now, using this initial solution, where the time-periodic vortex shedding has developed, run this simulation with frequent solution output to visualize the vortex shedding.
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
int main()
{
const double GAMMA = 1.4;
int NI,NJ,NK,ndims;
char ip_file_type[50];
FILE *in;
strcpy(ip_file_type,"ascii");
printf("Reading file \"solver.inp\"...\n");
in = fopen("solver.inp","r");
if (!in) {
printf("Error: Input file \"solver.inp\" not found.\n");
return(0);
} else {
char word[500];
fscanf(in,"%s",word);
if (!strcmp(word, "begin")){
while (strcmp(word, "end")){
fscanf(in,"%s",word);
if (!strcmp(word, "ndims")) {
fscanf(in,"%d",&ndims);
} else if (!strcmp(word, "size" )) {
fscanf(in,"%d",&NI);
fscanf(in,"%d",&NJ);
fscanf(in,"%d",&NK);
} else if (!strcmp(word, "ip_file_type")) {
fscanf(in,"%s",ip_file_type);
}
}
} else {
printf("Error: Illegal format in solver.inp. Crash and burn!\n");
return(0);
}
}
fclose(in);
if (ndims != 3) {
printf("Error: ndims is not 3 in solver.inp.\n");
return(0);
}
printf("Grid: %3d x %3d x %3d.\n",NI,NJ,NK);
double Lx = 16.0;
double Ly = 4.0;
double sf_x1 = 1.05;
double sf_x2 = 1.08;
double sf_y = 1.4;
int i,j,k;
double u = 0.1,
v = 0.0,
w = 0.0,
rho = 1.0,
P = 1.0/GAMMA;
double *x, *y, *z, *U;
double dx, dy, dz;
FILE *out;
x = (double*) calloc (NI , sizeof(double));
y = (double*) calloc (NJ , sizeof(double));
z = (double*) calloc (NK , sizeof(double));
U = (double*) calloc (5*NI*NJ*NK, sizeof(double));
x[NI/8] = -Lx/4;
x[7*NI/8] = 3*Lx/4;
dx = Lx / ((double)(6*NI/8));
for (i = NI/8 ; i < 7*NI/8; i++) x[i] = x[NI/8] + dx * (i-NI/8);
for (i = 7*NI/8; i < NI ; i++) x[i] = x[i-1] + sf_x2 * (x[i-1] - x[i-2]);
for (i = NI/8-1; i >= 0 ; i--) x[i] = x[i+1] - sf_x1 * (x[i+2] - x[i+1]);
y[NJ/8] = -Ly/2;
y[7*NJ/8] = Ly/2;
dy = Ly / ((double)(6*NJ/8));
for (j = NJ/8 ; j < 7*NJ/8; j++) y[j] = y[NJ/8] + dy * (j-NJ/8);
for (j = 7*NJ/8; j < NJ ; j++) y[j] = y[j-1] + sf_y * (y[j-1] - y[j-2]);
for (j = NJ/8-1; j >= 0 ; j--) y[j] = y[j+1] - sf_y * (y[j+2] - y[j+1]);
dz = 0.5 * (dx +dy);
for (k = 0; k < NK; k++) z[k] = (k-NK/2) * dz;
for (i = 0; i < NI; i++){
for (j = 0; j < NJ; j++){
for (k = 0; k < NK; k++){
int p = i + NI*j + NI*NJ*k;
U[5*p+0] = rho;
U[5*p+1] = rho*u;
U[5*p+2] = rho*v;
U[5*p+3] = rho*w;
U[5*p+4] = P/(GAMMA-1.0) + 0.5*rho*(u*u+v*v+w*w);
}
}
}
if (!strcmp(ip_file_type,"ascii")) {
printf("Writing ASCII initial solution file initial.inp\n");
out = fopen("initial.inp","w");
for (i = 0; i < NI; i++) fprintf(out,"%1.16E ",x[i]);
fprintf(out,"\n");
for (j = 0; j < NJ; j++) fprintf(out,"%1.16E ",y[j]);
fprintf(out,"\n");
for (k = 0; k < NK; k++) fprintf(out,"%1.16E ",z[k]);
fprintf(out,"\n");
for (k = 0; k < NK; k++) {
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = i + NK*j + NI*NJ*k;
fprintf(out,"%1.16E ",U[5*p+0]);
}
}
}
fprintf(out,"\n");
for (k = 0; k < NK; k++) {
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = i + NK*j + NI*NJ*k;
fprintf(out,"%1.16E ",U[5*p+1]);
}
}
}
fprintf(out,"\n");
for (k = 0; k < NK; k++) {
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = i + NK*j + NI*NJ*k;
fprintf(out,"%1.16E ",U[5*p+2]);
}
}
}
fprintf(out,"\n");
for (k = 0; k < NK; k++) {
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = i + NK*j + NI*NJ*k;
fprintf(out,"%1.16E ",U[5*p+3]);
}
}
}
fprintf(out,"\n");
for (k = 0; k < NK; k++) {
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = i + NK*j + NI*NJ*k;
fprintf(out,"%1.16E ",U[5*p+4]);
}
}
}
fprintf(out,"\n");
fclose(out);
} else if ((!strcmp(ip_file_type,"binary")) || (!strcmp(ip_file_type,"bin"))) {
printf("Writing binary initial solution file initial.inp\n");
out = fopen("initial.inp","wb");
fwrite(x,sizeof(double),NI,out);
fwrite(y,sizeof(double),NJ,out);
fwrite(z,sizeof(double),NK,out);
fwrite(U,sizeof(double),5*NI*NJ*NK,out);
fclose(out);
}
free(x);
free(y);
free(z);
free(U);
return(0);
}
Output:
Note that iproc is set to
8 4 1
in solver.inp (i.e., 8 processors along x, 4 processors along y, and 1 processor along z). Thus, this example should be run with 32 MPI ranks (or change iproc).
Please see the original example in the "Immersed Boundaries Examples" section for a full description of the output files and how to view them. The following only contains libROM-specific comments.
After running the code, there should be the following output files:
- 41 output file op_00000.bin, ..., op_00040.bin; these are the HyPar solutions.
- 41 output file op_rom_00000.bin, ..., op_rom_00040.bin; these are the predicted solutions from the DMD object(s).
All the files are binary (HyPar::op_file_format is set to binary in solver.inp).
The provided Python script (plotSolution.py) can be used to generate plots from the binary files that compare the HyPar and DMD solutions. Alternatively, HyPar::op_file_format can be set to tecplot3d, and Tecplot/VisIt or something similar can be used to plot the resulting text files.
The following figure shows the vortex shedding. The pressure is plotted in the overall domain, and the wake is shown by plotting the x-velocity, where it is negative. FOM (full-order model) refers to the HyPar solution, ROM (reduced-order model) refers to the DMD solution, and Diff is the difference between the two.
Wall clock times:
- PDE solution: 2413 seconds
- DMD training time: 2113 seconds
- DMD prediction/query time: 9.8 seconds
The L1, L2, and Linf norms of the diff between the HyPar and ROM solution at the final time are calculated and reported on screen (see below) as well as pde_rom_diff.dat:
400 96 3 8 4 1 4.0000000000000001E-02 2.2563355954629010E-05 2.4733914130219971E-05 2.4975703864253711E-04 4.5519722849999998E+03 4.5527609110000003E+03
The numbers are: number of grid points in each dimension (HyPar::dim_global), number of processors in each dimension (MPIVariables::iproc), time step size (HyPar::dt), L1, L2, and L-infinity norms of the diff (HyPar::rom_diff_norms), solver wall time (seconds) (i.e., not accounting for initialization, and cleaning up), and total wall time.
Expected screen output:
HyPar - Parallel (MPI) version with 32 processes
Compiled with PETSc time integration.
Allocated simulation object(s).
Reading solver inputs from file "solver.inp".
No. of dimensions : 3
No. of variables : 5
Domain size : 400 96 3
Processes along each dimension : 8 4 1
Exact solution domain size : 400 96 3
No. of ghosts pts : 3
No. of iter. : 10000
Restart iteration : 0
Time integration scheme : rk (44)
Spatial discretization scheme (hyperbolic) : weno5
Split hyperbolic flux term? : no
Interpolation type for hyperbolic term : components
Spatial discretization type (parabolic ) : nonconservative-2stage
Spatial discretization scheme (parabolic ) : 4
Time Step : 4.000000E-02
Check for conservation : no
Screen output iterations : 50
File output iterations : 250
Initial solution file type : binary
Initial solution read mode : serial
Solution file write mode : serial
Solution file format : binary
Overwrite solution file : no
Physical model : navierstokes3d
Immersed Body : cylinder.stl
Partitioning domain and allocating data arrays.
Reading array from binary file initial.inp (Serial mode).
Volume integral of the initial solution:
0: 2.9233368196521371E+02
1: 2.8593271918010952E+01
2: 9.8236287231872887E-03
3: -4.7954769269532492E-12
4: 5.2362439317196799E+02
Reading boundary conditions from boundary.inp.
Boundary subsonic-inflow: Along dimension 0 and face +1
Boundary subsonic-outflow: Along dimension 0 and face -1
Boundary subsonic-ambivalent: Along dimension 1 and face +1
Boundary subsonic-ambivalent: Along dimension 1 and face -1
Boundary periodic: Along dimension 2 and face +1
Boundary periodic: Along dimension 2 and face -1
6 boundary condition(s) read.
Immersed body read from cylinder.stl:
Number of facets: 628
Bounding box: [-1.0,1.0] X [-1.0,1.0] X [-5.0,5.0]
Number of grid points inside immersed body: 3264 ( 2.8%).
Number of immersed boundary points : 864 ( 0.8%).
Immersed body simulation mode : 2d (xy).
Initializing solvers.
Warning: File weno.inp not found. Using default parameters for WENO5/CRWENO5/HCWENO5 scheme.
Initializing physics. Model = "navierstokes3d"
Reading physical model inputs from file "physics.inp".
Writing solution file iblank_00000.bin.
Setting up time integration.
Setting up libROM interface.
libROM inputs and parameters:
reduced model dimensionality: 16
sampling frequency: 2
mode: train
type: DMD
save to file: true
local vector size: 18000
libROM DMD inputs:
number of samples per window: 1000
directory name for DMD onjects: DMD
Solving in time (from 0 to 10000 iterations)
Writing immersed body surface data file surface00000.dat.
Writing solution file op_00000.bin.
DMDROMObject::takeSample() - creating new DMD object, t=0.000000 (total: 1).
iter= 50 t=2.000E+00 CFL=8.485E-01 norm=6.2689E-05 wctime: 2.4E-01 (s)
iter= 100 t=4.000E+00 CFL=8.486E-01 norm=6.2661E-05 wctime: 2.5E-01 (s)
iter= 150 t=6.000E+00 CFL=8.486E-01 norm=6.2530E-05 wctime: 2.5E-01 (s)
iter= 200 t=8.000E+00 CFL=8.486E-01 norm=6.2243E-05 wctime: 2.5E-01 (s)
iter= 250 t=1.000E+01 CFL=8.487E-01 norm=6.1896E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00001.dat.
Writing solution file op_00001.bin.
iter= 300 t=1.200E+01 CFL=8.486E-01 norm=6.1456E-05 wctime: 2.5E-01 (s)
iter= 350 t=1.400E+01 CFL=8.486E-01 norm=6.0973E-05 wctime: 2.5E-01 (s)
iter= 400 t=1.600E+01 CFL=8.485E-01 norm=6.0543E-05 wctime: 2.5E-01 (s)
iter= 450 t=1.800E+01 CFL=8.484E-01 norm=6.0102E-05 wctime: 2.5E-01 (s)
iter= 500 t=2.000E+01 CFL=8.483E-01 norm=5.9813E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00002.dat.
Writing solution file op_00002.bin.
iter= 550 t=2.200E+01 CFL=8.483E-01 norm=5.9656E-05 wctime: 2.4E-01 (s)
iter= 600 t=2.400E+01 CFL=8.482E-01 norm=5.9581E-05 wctime: 2.5E-01 (s)
iter= 650 t=2.600E+01 CFL=8.484E-01 norm=5.9580E-05 wctime: 2.5E-01 (s)
iter= 700 t=2.800E+01 CFL=8.486E-01 norm=5.9716E-05 wctime: 2.5E-01 (s)
iter= 750 t=3.000E+01 CFL=8.488E-01 norm=5.9910E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00003.dat.
Writing solution file op_00003.bin.
iter= 800 t=3.200E+01 CFL=8.489E-01 norm=6.0099E-05 wctime: 2.5E-01 (s)
iter= 850 t=3.400E+01 CFL=8.489E-01 norm=6.0324E-05 wctime: 2.5E-01 (s)
iter= 900 t=3.600E+01 CFL=8.490E-01 norm=6.0541E-05 wctime: 2.5E-01 (s)
iter= 950 t=3.800E+01 CFL=8.490E-01 norm=6.0736E-05 wctime: 2.5E-01 (s)
iter= 1000 t=4.000E+01 CFL=8.491E-01 norm=6.0915E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00004.dat.
Writing solution file op_00004.bin.
iter= 1050 t=4.200E+01 CFL=8.490E-01 norm=6.1080E-05 wctime: 2.4E-01 (s)
iter= 1100 t=4.400E+01 CFL=8.490E-01 norm=6.1272E-05 wctime: 2.5E-01 (s)
iter= 1150 t=4.600E+01 CFL=8.489E-01 norm=6.1448E-05 wctime: 2.5E-01 (s)
iter= 1200 t=4.800E+01 CFL=8.488E-01 norm=6.1669E-05 wctime: 2.5E-01 (s)
iter= 1250 t=5.000E+01 CFL=8.486E-01 norm=6.1890E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00005.dat.
Writing solution file op_00005.bin.
iter= 1300 t=5.200E+01 CFL=8.484E-01 norm=6.2104E-05 wctime: 2.5E-01 (s)
iter= 1350 t=5.400E+01 CFL=8.484E-01 norm=6.2298E-05 wctime: 2.5E-01 (s)
iter= 1400 t=5.600E+01 CFL=8.485E-01 norm=6.2487E-05 wctime: 2.4E-01 (s)
iter= 1450 t=5.800E+01 CFL=8.486E-01 norm=6.2644E-05 wctime: 2.5E-01 (s)
iter= 1500 t=6.000E+01 CFL=8.486E-01 norm=6.2726E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00006.dat.
Writing solution file op_00006.bin.
iter= 1550 t=6.200E+01 CFL=8.486E-01 norm=6.2772E-05 wctime: 2.5E-01 (s)
iter= 1600 t=6.400E+01 CFL=8.487E-01 norm=6.2721E-05 wctime: 2.5E-01 (s)
iter= 1650 t=6.600E+01 CFL=8.487E-01 norm=6.2577E-05 wctime: 2.5E-01 (s)
iter= 1700 t=6.800E+01 CFL=8.487E-01 norm=6.2262E-05 wctime: 2.5E-01 (s)
iter= 1750 t=7.000E+01 CFL=8.486E-01 norm=6.1908E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00007.dat.
Writing solution file op_00007.bin.
iter= 1800 t=7.200E+01 CFL=8.486E-01 norm=6.1450E-05 wctime: 2.4E-01 (s)
iter= 1850 t=7.400E+01 CFL=8.486E-01 norm=6.1002E-05 wctime: 2.5E-01 (s)
iter= 1900 t=7.600E+01 CFL=8.485E-01 norm=6.0564E-05 wctime: 2.5E-01 (s)
iter= 1950 t=7.800E+01 CFL=8.485E-01 norm=6.0154E-05 wctime: 2.5E-01 (s)
iter= 2000 t=8.000E+01 CFL=8.484E-01 norm=5.9927E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00008.dat.
Writing solution file op_00008.bin.
DMDROMObject::takeSample() - creating new DMD object, t=80.000000 (total: 2).
iter= 2050 t=8.200E+01 CFL=8.484E-01 norm=5.9813E-05 wctime: 2.5E-01 (s)
iter= 2100 t=8.400E+01 CFL=8.484E-01 norm=5.9767E-05 wctime: 2.5E-01 (s)
iter= 2150 t=8.600E+01 CFL=8.486E-01 norm=5.9814E-05 wctime: 2.4E-01 (s)
iter= 2200 t=8.800E+01 CFL=8.488E-01 norm=5.9978E-05 wctime: 2.4E-01 (s)
iter= 2250 t=9.000E+01 CFL=8.489E-01 norm=6.0177E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00009.dat.
Writing solution file op_00009.bin.
iter= 2300 t=9.200E+01 CFL=8.490E-01 norm=6.0389E-05 wctime: 2.5E-01 (s)
iter= 2350 t=9.400E+01 CFL=8.490E-01 norm=6.0628E-05 wctime: 2.5E-01 (s)
iter= 2400 t=9.600E+01 CFL=8.491E-01 norm=6.0850E-05 wctime: 2.5E-01 (s)
iter= 2450 t=9.800E+01 CFL=8.491E-01 norm=6.1058E-05 wctime: 2.4E-01 (s)
iter= 2500 t=1.000E+02 CFL=8.491E-01 norm=6.1223E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00010.dat.
Writing solution file op_00010.bin.
iter= 2550 t=1.020E+02 CFL=8.491E-01 norm=6.1401E-05 wctime: 2.5E-01 (s)
iter= 2600 t=1.040E+02 CFL=8.490E-01 norm=6.1589E-05 wctime: 2.4E-01 (s)
iter= 2650 t=1.060E+02 CFL=8.489E-01 norm=6.1774E-05 wctime: 2.4E-01 (s)
iter= 2700 t=1.080E+02 CFL=8.487E-01 norm=6.1970E-05 wctime: 2.4E-01 (s)
iter= 2750 t=1.100E+02 CFL=8.485E-01 norm=6.2181E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00011.dat.
Writing solution file op_00011.bin.
iter= 2800 t=1.120E+02 CFL=8.484E-01 norm=6.2382E-05 wctime: 2.5E-01 (s)
iter= 2850 t=1.140E+02 CFL=8.484E-01 norm=6.2579E-05 wctime: 2.5E-01 (s)
iter= 2900 t=1.160E+02 CFL=8.485E-01 norm=6.2771E-05 wctime: 2.5E-01 (s)
iter= 2950 t=1.180E+02 CFL=8.486E-01 norm=6.2892E-05 wctime: 2.5E-01 (s)
iter= 3000 t=1.200E+02 CFL=8.486E-01 norm=6.2958E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00012.dat.
Writing solution file op_00012.bin.
iter= 3050 t=1.220E+02 CFL=8.486E-01 norm=6.3004E-05 wctime: 2.5E-01 (s)
iter= 3100 t=1.240E+02 CFL=8.487E-01 norm=6.2937E-05 wctime: 2.5E-01 (s)
iter= 3150 t=1.260E+02 CFL=8.487E-01 norm=6.2748E-05 wctime: 2.5E-01 (s)
iter= 3200 t=1.280E+02 CFL=8.487E-01 norm=6.2400E-05 wctime: 2.5E-01 (s)
iter= 3250 t=1.300E+02 CFL=8.487E-01 norm=6.2034E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00013.dat.
Writing solution file op_00013.bin.
iter= 3300 t=1.320E+02 CFL=8.487E-01 norm=6.1534E-05 wctime: 2.5E-01 (s)
iter= 3350 t=1.340E+02 CFL=8.486E-01 norm=6.1073E-05 wctime: 2.5E-01 (s)
iter= 3400 t=1.360E+02 CFL=8.485E-01 norm=6.0609E-05 wctime: 2.5E-01 (s)
iter= 3450 t=1.380E+02 CFL=8.484E-01 norm=6.0232E-05 wctime: 2.4E-01 (s)
iter= 3500 t=1.400E+02 CFL=8.484E-01 norm=6.0017E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00014.dat.
Writing solution file op_00014.bin.
iter= 3550 t=1.420E+02 CFL=8.483E-01 norm=5.9886E-05 wctime: 2.5E-01 (s)
iter= 3600 t=1.440E+02 CFL=8.485E-01 norm=5.9852E-05 wctime: 2.5E-01 (s)
iter= 3650 t=1.460E+02 CFL=8.487E-01 norm=5.9925E-05 wctime: 2.5E-01 (s)
iter= 3700 t=1.480E+02 CFL=8.489E-01 norm=6.0075E-05 wctime: 2.5E-01 (s)
iter= 3750 t=1.500E+02 CFL=8.490E-01 norm=6.0253E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00015.dat.
Writing solution file op_00015.bin.
iter= 3800 t=1.520E+02 CFL=8.490E-01 norm=6.0469E-05 wctime: 2.5E-01 (s)
iter= 3850 t=1.540E+02 CFL=8.491E-01 norm=6.0715E-05 wctime: 2.5E-01 (s)
iter= 3900 t=1.560E+02 CFL=8.491E-01 norm=6.0932E-05 wctime: 2.5E-01 (s)
iter= 3950 t=1.580E+02 CFL=8.492E-01 norm=6.1130E-05 wctime: 2.5E-01 (s)
iter= 4000 t=1.600E+02 CFL=8.491E-01 norm=6.1276E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00016.dat.
Writing solution file op_00016.bin.
DMDROMObject::takeSample() - creating new DMD object, t=160.000000 (total: 3).
iter= 4050 t=1.620E+02 CFL=8.491E-01 norm=6.1448E-05 wctime: 2.5E-01 (s)
iter= 4100 t=1.640E+02 CFL=8.490E-01 norm=6.1628E-05 wctime: 2.5E-01 (s)
iter= 4150 t=1.660E+02 CFL=8.489E-01 norm=6.1825E-05 wctime: 2.5E-01 (s)
iter= 4200 t=1.680E+02 CFL=8.487E-01 norm=6.2024E-05 wctime: 2.5E-01 (s)
iter= 4250 t=1.700E+02 CFL=8.485E-01 norm=6.2230E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00017.dat.
Writing solution file op_00017.bin.
iter= 4300 t=1.720E+02 CFL=8.484E-01 norm=6.2415E-05 wctime: 2.5E-01 (s)
iter= 4350 t=1.740E+02 CFL=8.485E-01 norm=6.2617E-05 wctime: 2.5E-01 (s)
iter= 4400 t=1.760E+02 CFL=8.486E-01 norm=6.2797E-05 wctime: 2.4E-01 (s)
iter= 4450 t=1.780E+02 CFL=8.486E-01 norm=6.2891E-05 wctime: 2.5E-01 (s)
iter= 4500 t=1.800E+02 CFL=8.487E-01 norm=6.2958E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00018.dat.
Writing solution file op_00018.bin.
iter= 4550 t=1.820E+02 CFL=8.487E-01 norm=6.2963E-05 wctime: 2.5E-01 (s)
iter= 4600 t=1.840E+02 CFL=8.488E-01 norm=6.2866E-05 wctime: 2.5E-01 (s)
iter= 4650 t=1.860E+02 CFL=8.487E-01 norm=6.2637E-05 wctime: 2.4E-01 (s)
iter= 4700 t=1.880E+02 CFL=8.487E-01 norm=6.2302E-05 wctime: 2.4E-01 (s)
iter= 4750 t=1.900E+02 CFL=8.487E-01 norm=6.1897E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00019.dat.
Writing solution file op_00019.bin.
iter= 4800 t=1.920E+02 CFL=8.486E-01 norm=6.1409E-05 wctime: 2.5E-01 (s)
iter= 4850 t=1.940E+02 CFL=8.486E-01 norm=6.0986E-05 wctime: 2.5E-01 (s)
iter= 4900 t=1.960E+02 CFL=8.485E-01 norm=6.0557E-05 wctime: 2.4E-01 (s)
iter= 4950 t=1.980E+02 CFL=8.485E-01 norm=6.0232E-05 wctime: 2.5E-01 (s)
iter= 5000 t=2.000E+02 CFL=8.484E-01 norm=6.0050E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00020.dat.
Writing solution file op_00020.bin.
iter= 5050 t=2.020E+02 CFL=8.483E-01 norm=5.9962E-05 wctime: 2.4E-01 (s)
iter= 5100 t=2.040E+02 CFL=8.486E-01 norm=5.9987E-05 wctime: 2.5E-01 (s)
iter= 5150 t=2.060E+02 CFL=8.488E-01 norm=6.0092E-05 wctime: 2.5E-01 (s)
iter= 5200 t=2.080E+02 CFL=8.489E-01 norm=6.0260E-05 wctime: 2.5E-01 (s)
iter= 5250 t=2.100E+02 CFL=8.490E-01 norm=6.0449E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00021.dat.
Writing solution file op_00021.bin.
iter= 5300 t=2.120E+02 CFL=8.491E-01 norm=6.0672E-05 wctime: 2.5E-01 (s)
iter= 5350 t=2.140E+02 CFL=8.492E-01 norm=6.0920E-05 wctime: 2.4E-01 (s)
iter= 5400 t=2.160E+02 CFL=8.492E-01 norm=6.1150E-05 wctime: 2.4E-01 (s)
iter= 5450 t=2.180E+02 CFL=8.492E-01 norm=6.1354E-05 wctime: 2.4E-01 (s)
iter= 5500 t=2.200E+02 CFL=8.491E-01 norm=6.1509E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00022.dat.
Writing solution file op_00022.bin.
iter= 5550 t=2.220E+02 CFL=8.491E-01 norm=6.1693E-05 wctime: 2.4E-01 (s)
iter= 5600 t=2.240E+02 CFL=8.490E-01 norm=6.1865E-05 wctime: 2.5E-01 (s)
iter= 5650 t=2.260E+02 CFL=8.489E-01 norm=6.2062E-05 wctime: 2.5E-01 (s)
iter= 5700 t=2.280E+02 CFL=8.487E-01 norm=6.2269E-05 wctime: 2.5E-01 (s)
iter= 5750 t=2.300E+02 CFL=8.485E-01 norm=6.2474E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00023.dat.
Writing solution file op_00023.bin.
iter= 5800 t=2.320E+02 CFL=8.485E-01 norm=6.2655E-05 wctime: 2.5E-01 (s)
iter= 5850 t=2.340E+02 CFL=8.485E-01 norm=6.2846E-05 wctime: 2.5E-01 (s)
iter= 5900 t=2.360E+02 CFL=8.486E-01 norm=6.3002E-05 wctime: 2.5E-01 (s)
iter= 5950 t=2.380E+02 CFL=8.487E-01 norm=6.3078E-05 wctime: 2.5E-01 (s)
iter= 6000 t=2.400E+02 CFL=8.487E-01 norm=6.3127E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00024.dat.
Writing solution file op_00024.bin.
DMDROMObject::takeSample() - creating new DMD object, t=240.000000 (total: 4).
iter= 6050 t=2.420E+02 CFL=8.487E-01 norm=6.3091E-05 wctime: 2.5E-01 (s)
iter= 6100 t=2.440E+02 CFL=8.487E-01 norm=6.2975E-05 wctime: 2.5E-01 (s)
iter= 6150 t=2.460E+02 CFL=8.488E-01 norm=6.2678E-05 wctime: 2.5E-01 (s)
iter= 6200 t=2.480E+02 CFL=8.488E-01 norm=6.2328E-05 wctime: 2.4E-01 (s)
iter= 6250 t=2.500E+02 CFL=8.487E-01 norm=6.1872E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00025.dat.
Writing solution file op_00025.bin.
iter= 6300 t=2.520E+02 CFL=8.487E-01 norm=6.1387E-05 wctime: 2.4E-01 (s)
iter= 6350 t=2.540E+02 CFL=8.486E-01 norm=6.0961E-05 wctime: 2.5E-01 (s)
iter= 6400 t=2.560E+02 CFL=8.485E-01 norm=6.0524E-05 wctime: 2.4E-01 (s)
iter= 6450 t=2.580E+02 CFL=8.484E-01 norm=6.0234E-05 wctime: 2.4E-01 (s)
iter= 6500 t=2.600E+02 CFL=8.483E-01 norm=6.0063E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00026.dat.
Writing solution file op_00026.bin.
iter= 6550 t=2.620E+02 CFL=8.484E-01 norm=5.9993E-05 wctime: 2.4E-01 (s)
iter= 6600 t=2.640E+02 CFL=8.486E-01 norm=6.0026E-05 wctime: 2.4E-01 (s)
iter= 6650 t=2.660E+02 CFL=8.488E-01 norm=6.0125E-05 wctime: 2.4E-01 (s)
iter= 6700 t=2.680E+02 CFL=8.490E-01 norm=6.0274E-05 wctime: 2.4E-01 (s)
iter= 6750 t=2.700E+02 CFL=8.491E-01 norm=6.0465E-05 wctime: 2.4E-01 (s)
Writing immersed body surface data file surface00027.dat.
Writing solution file op_00027.bin.
iter= 6800 t=2.720E+02 CFL=8.491E-01 norm=6.0706E-05 wctime: 2.4E-01 (s)
iter= 6850 t=2.740E+02 CFL=8.492E-01 norm=6.0943E-05 wctime: 2.5E-01 (s)
iter= 6900 t=2.760E+02 CFL=8.492E-01 norm=6.1150E-05 wctime: 2.5E-01 (s)
iter= 6950 t=2.780E+02 CFL=8.492E-01 norm=6.1338E-05 wctime: 2.5E-01 (s)
iter= 7000 t=2.800E+02 CFL=8.492E-01 norm=6.1499E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00028.dat.
Writing solution file op_00028.bin.
iter= 7050 t=2.820E+02 CFL=8.491E-01 norm=6.1682E-05 wctime: 2.4E-01 (s)
iter= 7100 t=2.840E+02 CFL=8.490E-01 norm=6.1870E-05 wctime: 2.5E-01 (s)
iter= 7150 t=2.860E+02 CFL=8.488E-01 norm=6.2073E-05 wctime: 2.5E-01 (s)
iter= 7200 t=2.880E+02 CFL=8.486E-01 norm=6.2266E-05 wctime: 2.4E-01 (s)
iter= 7250 t=2.900E+02 CFL=8.484E-01 norm=6.2455E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00029.dat.
Writing solution file op_00029.bin.
iter= 7300 t=2.920E+02 CFL=8.485E-01 norm=6.2654E-05 wctime: 2.5E-01 (s)
iter= 7350 t=2.940E+02 CFL=8.486E-01 norm=6.2862E-05 wctime: 2.5E-01 (s)
iter= 7400 t=2.960E+02 CFL=8.486E-01 norm=6.2971E-05 wctime: 2.5E-01 (s)
iter= 7450 t=2.980E+02 CFL=8.487E-01 norm=6.3026E-05 wctime: 2.4E-01 (s)
iter= 7500 t=3.000E+02 CFL=8.487E-01 norm=6.3058E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00030.dat.
Writing solution file op_00030.bin.
iter= 7550 t=3.020E+02 CFL=8.488E-01 norm=6.3002E-05 wctime: 2.5E-01 (s)
iter= 7600 t=3.040E+02 CFL=8.488E-01 norm=6.2842E-05 wctime: 2.5E-01 (s)
iter= 7650 t=3.060E+02 CFL=8.488E-01 norm=6.2509E-05 wctime: 2.5E-01 (s)
iter= 7700 t=3.080E+02 CFL=8.487E-01 norm=6.2137E-05 wctime: 2.5E-01 (s)
iter= 7750 t=3.100E+02 CFL=8.487E-01 norm=6.1661E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00031.dat.
Writing solution file op_00031.bin.
iter= 7800 t=3.120E+02 CFL=8.486E-01 norm=6.1223E-05 wctime: 2.5E-01 (s)
iter= 7850 t=3.140E+02 CFL=8.486E-01 norm=6.0814E-05 wctime: 2.5E-01 (s)
iter= 7900 t=3.160E+02 CFL=8.485E-01 norm=6.0434E-05 wctime: 2.5E-01 (s)
iter= 7950 t=3.180E+02 CFL=8.484E-01 norm=6.0208E-05 wctime: 2.5E-01 (s)
iter= 8000 t=3.200E+02 CFL=8.484E-01 norm=6.0083E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00032.dat.
Writing solution file op_00032.bin.
DMDROMObject::takeSample() - creating new DMD object, t=320.000000 (total: 5).
iter= 8050 t=3.220E+02 CFL=8.485E-01 norm=6.0069E-05 wctime: 2.5E-01 (s)
iter= 8100 t=3.240E+02 CFL=8.487E-01 norm=6.0140E-05 wctime: 2.5E-01 (s)
iter= 8150 t=3.260E+02 CFL=8.489E-01 norm=6.0286E-05 wctime: 2.5E-01 (s)
iter= 8200 t=3.280E+02 CFL=8.490E-01 norm=6.0462E-05 wctime: 2.4E-01 (s)
iter= 8250 t=3.300E+02 CFL=8.491E-01 norm=6.0654E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00033.dat.
Writing solution file op_00033.bin.
iter= 8300 t=3.320E+02 CFL=8.492E-01 norm=6.0878E-05 wctime: 2.4E-01 (s)
iter= 8350 t=3.340E+02 CFL=8.492E-01 norm=6.1124E-05 wctime: 2.4E-01 (s)
iter= 8400 t=3.360E+02 CFL=8.492E-01 norm=6.1342E-05 wctime: 2.4E-01 (s)
iter= 8450 t=3.380E+02 CFL=8.492E-01 norm=6.1513E-05 wctime: 2.4E-01 (s)
iter= 8500 t=3.400E+02 CFL=8.492E-01 norm=6.1691E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00034.dat.
Writing solution file op_00034.bin.
iter= 8550 t=3.420E+02 CFL=8.491E-01 norm=6.1873E-05 wctime: 2.5E-01 (s)
iter= 8600 t=3.440E+02 CFL=8.490E-01 norm=6.2068E-05 wctime: 2.5E-01 (s)
iter= 8650 t=3.460E+02 CFL=8.488E-01 norm=6.2277E-05 wctime: 2.5E-01 (s)
iter= 8700 t=3.480E+02 CFL=8.486E-01 norm=6.2496E-05 wctime: 2.5E-01 (s)
iter= 8750 t=3.500E+02 CFL=8.485E-01 norm=6.2689E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00035.dat.
Writing solution file op_00035.bin.
iter= 8800 t=3.520E+02 CFL=8.485E-01 norm=6.2868E-05 wctime: 2.4E-01 (s)
iter= 8850 t=3.540E+02 CFL=8.486E-01 norm=6.3045E-05 wctime: 2.4E-01 (s)
iter= 8900 t=3.560E+02 CFL=8.487E-01 norm=6.3141E-05 wctime: 2.5E-01 (s)
iter= 8950 t=3.580E+02 CFL=8.487E-01 norm=6.3183E-05 wctime: 2.5E-01 (s)
iter= 9000 t=3.600E+02 CFL=8.487E-01 norm=6.3180E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00036.dat.
Writing solution file op_00036.bin.
iter= 9050 t=3.620E+02 CFL=8.487E-01 norm=6.3096E-05 wctime: 2.5E-01 (s)
iter= 9100 t=3.640E+02 CFL=8.488E-01 norm=6.2862E-05 wctime: 2.5E-01 (s)
iter= 9150 t=3.660E+02 CFL=8.488E-01 norm=6.2497E-05 wctime: 2.5E-01 (s)
iter= 9200 t=3.680E+02 CFL=8.487E-01 norm=6.2085E-05 wctime: 2.5E-01 (s)
iter= 9250 t=3.700E+02 CFL=8.487E-01 norm=6.1596E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00037.dat.
Writing solution file op_00037.bin.
iter= 9300 t=3.720E+02 CFL=8.486E-01 norm=6.1158E-05 wctime: 2.5E-01 (s)
iter= 9350 t=3.740E+02 CFL=8.485E-01 norm=6.0715E-05 wctime: 2.5E-01 (s)
iter= 9400 t=3.760E+02 CFL=8.485E-01 norm=6.0374E-05 wctime: 2.5E-01 (s)
iter= 9450 t=3.780E+02 CFL=8.484E-01 norm=6.0178E-05 wctime: 2.4E-01 (s)
iter= 9500 t=3.800E+02 CFL=8.483E-01 norm=6.0074E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00038.dat.
Writing solution file op_00038.bin.
iter= 9550 t=3.820E+02 CFL=8.486E-01 norm=6.0074E-05 wctime: 2.5E-01 (s)
iter= 9600 t=3.840E+02 CFL=8.488E-01 norm=6.0152E-05 wctime: 2.4E-01 (s)
iter= 9650 t=3.860E+02 CFL=8.490E-01 norm=6.0292E-05 wctime: 2.5E-01 (s)
iter= 9700 t=3.880E+02 CFL=8.491E-01 norm=6.0468E-05 wctime: 2.5E-01 (s)
iter= 9750 t=3.900E+02 CFL=8.491E-01 norm=6.0681E-05 wctime: 2.5E-01 (s)
Writing immersed body surface data file surface00039.dat.
Writing solution file op_00039.bin.
iter= 9800 t=3.920E+02 CFL=8.492E-01 norm=6.0919E-05 wctime: 2.5E-01 (s)
iter= 9850 t=3.940E+02 CFL=8.492E-01 norm=6.1130E-05 wctime: 2.5E-01 (s)
iter= 9900 t=3.960E+02 CFL=8.492E-01 norm=6.1325E-05 wctime: 2.5E-01 (s)
iter= 9950 t=3.980E+02 CFL=8.492E-01 norm=6.1487E-05 wctime: 2.5E-01 (s)
iter= 10000 t=4.000E+02 CFL=8.491E-01 norm=6.1654E-05 wctime: 2.5E-01 (s)
Completed time integration (Final time: 400.000000), total wctime: 2413.348070 (seconds).
Writing immersed body surface data file surface00040.dat.
Writing solution file op_00040.bin.
libROM: Training ROM.
DMDROMObject::train() - training DMD object 0 with 1001 samples.
Using 16 basis vectors out of 1000.
DMDROMObject::train() - training DMD object 1 with 1001 samples.
Using 16 basis vectors out of 1000.
DMDROMObject::train() - training DMD object 2 with 1001 samples.
Using 16 basis vectors out of 1000.
DMDROMObject::train() - training DMD object 3 with 1001 samples.
Using 16 basis vectors out of 1000.
DMDROMObject::train() - training DMD object 4 with 1000 samples.
Using 16 basis vectors out of 999.
libROM: total training wallclock time: 2112.749892 (seconds).
libROM: Predicting solution at time 0.0000e+00 using ROM.
libROM: wallclock time: 0.233794 (seconds).
Writing solution file op_rom_00000.bin.
libROM: Predicting solution at time 1.0000e+01 using ROM.
libROM: wallclock time: 0.231340 (seconds).
Writing solution file op_rom_00001.bin.
libROM: Predicting solution at time 2.0000e+01 using ROM.
libROM: wallclock time: 0.234202 (seconds).
Writing solution file op_rom_00002.bin.
libROM: Predicting solution at time 3.0000e+01 using ROM.
libROM: wallclock time: 0.237055 (seconds).
Writing solution file op_rom_00003.bin.
libROM: Predicting solution at time 4.0000e+01 using ROM.
libROM: wallclock time: 0.236783 (seconds).
Writing solution file op_rom_00004.bin.
libROM: Predicting solution at time 5.0000e+01 using ROM.
libROM: wallclock time: 0.232317 (seconds).
Writing solution file op_rom_00005.bin.
libROM: Predicting solution at time 6.0000e+01 using ROM.
libROM: wallclock time: 0.237462 (seconds).
Writing solution file op_rom_00006.bin.
libROM: Predicting solution at time 7.0000e+01 using ROM.
libROM: wallclock time: 0.241502 (seconds).
Writing solution file op_rom_00007.bin.
libROM: Predicting solution at time 8.0000e+01 using ROM.
libROM: wallclock time: 0.246036 (seconds).
Writing solution file op_rom_00008.bin.
libROM: Predicting solution at time 9.0000e+01 using ROM.
libROM: wallclock time: 0.242724 (seconds).
Writing solution file op_rom_00009.bin.
libROM: Predicting solution at time 1.0000e+02 using ROM.
libROM: wallclock time: 0.244469 (seconds).
Writing solution file op_rom_00010.bin.
libROM: Predicting solution at time 1.1000e+02 using ROM.
libROM: wallclock time: 0.239162 (seconds).
Writing solution file op_rom_00011.bin.
libROM: Predicting solution at time 1.2000e+02 using ROM.
libROM: wallclock time: 0.239186 (seconds).
Writing solution file op_rom_00012.bin.
libROM: Predicting solution at time 1.3000e+02 using ROM.
libROM: wallclock time: 0.239854 (seconds).
Writing solution file op_rom_00013.bin.
libROM: Predicting solution at time 1.4000e+02 using ROM.
libROM: wallclock time: 0.240379 (seconds).
Writing solution file op_rom_00014.bin.
libROM: Predicting solution at time 1.5000e+02 using ROM.
libROM: wallclock time: 0.239745 (seconds).
Writing solution file op_rom_00015.bin.
libROM: Predicting solution at time 1.6000e+02 using ROM.
libROM: wallclock time: 0.241440 (seconds).
Writing solution file op_rom_00016.bin.
libROM: Predicting solution at time 1.7000e+02 using ROM.
libROM: wallclock time: 0.247398 (seconds).
Writing solution file op_rom_00017.bin.
libROM: Predicting solution at time 1.8000e+02 using ROM.
libROM: wallclock time: 0.244496 (seconds).
Writing solution file op_rom_00018.bin.
libROM: Predicting solution at time 1.9000e+02 using ROM.
libROM: wallclock time: 0.250613 (seconds).
Writing solution file op_rom_00019.bin.
libROM: Predicting solution at time 2.0000e+02 using ROM.
libROM: wallclock time: 0.246348 (seconds).
Writing solution file op_rom_00020.bin.
libROM: Predicting solution at time 2.1000e+02 using ROM.
libROM: wallclock time: 0.239400 (seconds).
Writing solution file op_rom_00021.bin.
libROM: Predicting solution at time 2.2000e+02 using ROM.
libROM: wallclock time: 0.239655 (seconds).
Writing solution file op_rom_00022.bin.
libROM: Predicting solution at time 2.3000e+02 using ROM.
libROM: wallclock time: 0.240208 (seconds).
Writing solution file op_rom_00023.bin.
libROM: Predicting solution at time 2.4000e+02 using ROM.
libROM: wallclock time: 0.243463 (seconds).
Writing solution file op_rom_00024.bin.
libROM: Predicting solution at time 2.5000e+02 using ROM.
libROM: wallclock time: 0.246869 (seconds).
Writing solution file op_rom_00025.bin.
libROM: Predicting solution at time 2.6000e+02 using ROM.
libROM: wallclock time: 0.238274 (seconds).
Writing solution file op_rom_00026.bin.
libROM: Predicting solution at time 2.7000e+02 using ROM.
libROM: wallclock time: 0.237310 (seconds).
Writing solution file op_rom_00027.bin.
libROM: Predicting solution at time 2.8000e+02 using ROM.
libROM: wallclock time: 0.236455 (seconds).
Writing solution file op_rom_00028.bin.
libROM: Predicting solution at time 2.9000e+02 using ROM.
libROM: wallclock time: 0.236396 (seconds).
Writing solution file op_rom_00029.bin.
libROM: Predicting solution at time 3.0000e+02 using ROM.
libROM: wallclock time: 0.239319 (seconds).
Writing solution file op_rom_00030.bin.
libROM: Predicting solution at time 3.1000e+02 using ROM.
libROM: wallclock time: 0.236808 (seconds).
Writing solution file op_rom_00031.bin.
libROM: Predicting solution at time 3.2000e+02 using ROM.
libROM: wallclock time: 0.238982 (seconds).
Writing solution file op_rom_00032.bin.
libROM: Predicting solution at time 3.3000e+02 using ROM.
libROM: wallclock time: 0.237195 (seconds).
Writing solution file op_rom_00033.bin.
libROM: Predicting solution at time 3.4000e+02 using ROM.
libROM: wallclock time: 0.238842 (seconds).
Writing solution file op_rom_00034.bin.
libROM: Predicting solution at time 3.5000e+02 using ROM.
libROM: wallclock time: 0.243906 (seconds).
Writing solution file op_rom_00035.bin.
libROM: Predicting solution at time 3.6000e+02 using ROM.
libROM: wallclock time: 0.241236 (seconds).
Writing solution file op_rom_00036.bin.
libROM: Predicting solution at time 3.7000e+02 using ROM.
libROM: wallclock time: 0.242927 (seconds).
Writing solution file op_rom_00037.bin.
libROM: Predicting solution at time 3.8000e+02 using ROM.
libROM: wallclock time: 0.236618 (seconds).
Writing solution file op_rom_00038.bin.
libROM: Predicting solution at time 3.9000e+02 using ROM.
libROM: wallclock time: 0.238566 (seconds).
Writing solution file op_rom_00039.bin.
libROM: Predicting solution at time 4.0000e+02 using ROM.
libROM: wallclock time: 0.238102 (seconds).
libROM: Calculating diff between PDE and ROM solutions.
Writing solution file op_rom_00040.bin.
libROM: total prediction/query wallclock time: 9.836836 (seconds).
libROMInterface::saveROM() - saving ROM objects.
Saving DMD object with filename root DMD/dmdobj_0000.
Saving DMD object with filename root DMD/dmdobj_0001.
Saving DMD object with filename root DMD/dmdobj_0002.
Saving DMD object with filename root DMD/dmdobj_0003.
Saving DMD object with filename root DMD/dmdobj_0004.
Norms of the diff between ROM and PDE solutions for domain 0:
L1 Norm : 2.2563355954629010E-05
L2 Norm : 2.4733914130219971E-05
Linfinity Norm : 2.4975703864253711E-04
Solver runtime (in seconds): 4.5519722849999998E+03
Total runtime (in seconds): 4.5527609110000003E+03
Deallocating arrays.
Finished.