2D Linear Advection - Sine Wave with Spatially-Varying Advection Speed
Location: hypar/Examples/2D/LinearAdvection/SineWave_NonConstantAdvection/case_01 (This directory contains all the input files needed to run this case.)
Governing equations: 2D Linear Advection Equation (linearadr.h)
Domain: \(0 \le x,y < 1\), "periodic" (_PERIODIC_) boundary conditions on all boundaries.
Initial solution: \(u\left(x,y,0\right) = u_0\left(x,y\right)= \cos\left(4\pi y\right)\)
Advection speed: \(a_x\left(x,y\right) = \sin\left(4\pi y\right)\), \(a_y\left(x,y\right) = -\cos\left(4\pi x\right)\)
Numerical Method:
- Spatial discretization (hyperbolic): 5th order CRWENO (Interp1PrimFifthOrderCRWENO())
- Time integration: RK4 (TimeRK(), _RK_44_)
Input files required:
solver.inp
begin
ndims 2
nvars 1
size 128 128
iproc 4 4
ghost 3
n_iter 1000
restart_iter 0
time_scheme rk
time_scheme_type 44
hyp_space_scheme crweno5
hyp_interp_type components
dt 0.004
conservation_check yes
screen_op_iter 10
file_op_iter 10
op_file_format tecplot2d
ip_file_type binary
input_mode serial
output_mode serial
op_overwrite no
model linear-advection-diffusion-reaction
end
boundary.inp
4
periodic 0 1 0 0 0 1
periodic 0 -1 0 0 0 1
periodic 1 1 0 1 0 0
periodic 1 -1 0 1 0 0
physics.inp (specifies filename for advection field)
begin
advection_filename advection
end
Note: Do not include the ".inp" extension in the filename above.
lusolver.inp (optional)
begin
reducedsolvetype jacobi
evaluate_norm 1
maxiter 10
atol 1e-12
rtol 1e-10
verbose 0
end
weno.inp (optional)
begin
mapped 0
borges 0
yc 1
no_limiting 0
epsilon 9.9999999999999995e-07
p 2.0000000000000000e+00
rc 2.9999999999999999e-01
xi 1.0000000000000000e-03
tol 9.9999999999999998e-17
end
To generate initial.inp and advection.inp, compile and run the following code in the run directory.
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
int main()
{
const double pi = 4.0*atan(1.0);
int NI, NJ, ndims;
char ip_file_type[50];
strcpy(ip_file_type,"ascii");
FILE *in;
printf("Reading file \"solver.inp\"...\n");
in = fopen("solver.inp","r");
if (!in) {
fprintf(stderr,"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);
} else if (!strcmp(word, "ip_file_type")) {
fscanf(in,"%s",ip_file_type);
}
}
} else {
fprintf(stderr,"Error: Illegal format in solver.inp. Crash and burn!\n");
return(0);
}
}
fclose(in);
char adv_filename[500] = "none";
int flag = 0;
printf("Reading file \"physics.inp\"...\n");
in = fopen("physics.inp","r");
if (!in) {
printf("Error: Input file \"physics.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, "advection_filename")) {
fscanf(in,"%s", adv_filename);
flag = 1;
}
}
} else {
printf("Error: Illegal format in solver.inp. Crash and burn!\n");
}
}
fclose(in);
if (flag == 0) {
printf("Error: Input \"advection_filename\" not found in physics.inp file.\n");
return 0;
}
strcat(adv_filename, ".inp");
if (ndims != 2) {
fprintf(stderr,"ndims is not 2 in solver.inp. this code is to generate 2D initial conditions\n");
return(0);
}
printf("Grid: %d, %d\n",NI,NJ);
int i,j;
double dx = 1.0 / ((double)NI);
double dy = 1.0 / ((double)NJ);
double *x, *y, *u, *a;
x = (double*) calloc (NI , sizeof(double));
y = (double*) calloc (NJ , sizeof(double));
u = (double*) calloc (NI*NJ, sizeof(double));
a = (double*) calloc (ndims*NI*NJ, sizeof(double));
for (i = 0; i < NI; i++) {
for (j = 0; j < NJ; j++) {
x[i] = (i+0.5)*dx;
y[j] = (j+0.5)*dy;
int p = NI*j + i;
u[p] = cos(4*pi*y[j]);
a[ndims*p+0] = sin(4*pi*y[j]);
a[ndims*p+1] = -cos(4*pi*x[i]);
}
}
FILE *out;
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,"%lf ",x[i]);
fprintf(out,"\n");
for (j = 0; j < NJ; j++) fprintf(out,"%lf ",y[j]);
fprintf(out,"\n");
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = NJ*i + j;
fprintf(out,"%lf ",u[p]);
}
}
fprintf(out,"\n");
fclose(out);
printf("Writing ASCII advection field file %s\n", adv_filename);
out = fopen(adv_filename,"w");
for (i = 0; i < NI; i++) fprintf(out,"%lf ",x[i]);
fprintf(out,"\n");
for (j = 0; j < NJ; j++) fprintf(out,"%lf ",y[j]);
fprintf(out,"\n");
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = NJ*i + j;
fprintf(out,"%lf ",a[ndims*p+0]);
}
}
fprintf(out,"\n");
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = NJ*i + j;
fprintf(out,"%lf ",a[ndims*p+1]);
}
}
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(u,sizeof(double),NI*NJ,out);
fclose(out);
printf("Writing binary advection field file %s\n", adv_filename);
out = fopen(adv_filename,"wb");
fwrite(x,sizeof(double),NI,out);
fwrite(y,sizeof(double),NJ,out);
fwrite(a,sizeof(double),ndims*NI*NJ,out);
fclose(out);
}
free(x);
free(y);
free(u);
free(a);
return(0);
}
Output:
Note that iproc is set to
4 4
in solver.inp (i.e., 4 processors along x, and 2 processors along y). Thus, this example should be run with 16 MPI ranks (or change iproc).
After running the code, there should be 101 output files op_00000.dat, op_00001.dat, ... op_00100.dat; the first one is the solution at \(t=0\) and the final one is the solution at \(t=4\). Since HyPar::op_overwrite is set to no in solver.inp, separate files are written for solutions at each output time.
HyPar::op_file_format is set to tecplot2d in solver.inp, and thus, all the files are in a format that Tecplot (http://www.tecplot.com/) or other visualization software supporting the Tecplot format (e.g. VisIt - https://wci.llnl.gov/simulation/computer-codes/visit/) can read. In these files, the first two lines are the Tecplot headers, after which the data is written out as: the first two columns are grid indices, the next two columns are x and y coordinates, and the final column is the solution. HyPar::op_file_format can be set to text to get the solution files in plain text format (which can be read in and visualized in MATLAB for example).
The following animation was generated from the solution files:
In addition to the usual output files, the linear advection physics module writes out the following files:
- advection_00000.dat, ..., advection_00100.dat: These files share the same format as the solution output files op_*.dat and contains the advection field \(a_x\left(x,y\right), a_y\left(x,y\right)\). The following figure shows the vector plot of the velocity field:
Since HyPar::ConservationCheck is set to yes in solver.inp, the code checks for conservation error and prints it to screen, as well as the file conservation.dat:
128 128 4 4 4.0000000000000001E-03 5.6469145494602441E-17
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), and conservation error (HyPar::ConservationError).
Expected screen output:
HyPar - Parallel (MPI) version with 16 processes
Compiled with PETSc time integration.
Allocated simulation object(s).
Reading solver inputs from file "solver.inp".
No. of dimensions : 2
No. of variables : 1
Domain size : 128 128
Processes along each dimension : 4 4
No. of ghosts pts : 3
No. of iter. : 1000
Restart iteration : 0
Time integration scheme : rk (44)
Spatial discretization scheme (hyperbolic) : crweno5
Split hyperbolic flux term? : no
Interpolation type for hyperbolic term : components
Spatial discretization type (parabolic ) : nonconservative-1stage
Spatial discretization scheme (parabolic ) : 2
Time Step : 4.000000E-03
Check for conservation : yes
Screen output iterations : 10
File output iterations : 10
Initial solution file type : binary
Initial solution read mode : serial
Solution file write mode : serial
Solution file format : tecplot2d
Overwrite solution file : no
Physical model : linear-advection-diffusion-reaction
Partitioning domain.
Allocating data arrays.
Reading array from binary file initial.inp (Serial mode).
Volume integral of the initial solution:
0: 0.0000000000000000E+00
Reading boundary conditions from boundary.inp.
Boundary periodic: Along dimension 0 and face +1
Boundary periodic: Along dimension 0 and face -1
Boundary periodic: Along dimension 1 and face +1
Boundary periodic: Along dimension 1 and face -1
4 boundary condition(s) read.
Initializing solvers.
Reading WENO parameters from weno.inp.
Initializing physics. Model = "linear-advection-diffusion-reaction"
Reading physical model inputs from file "physics.inp".
Reading advection field from advection.
Reading array from binary file advection.inp (Serial mode).
Setting up time integration.
Solving in time (from 0 to 1000 iterations)
Writing solution file advection_field_00000.dat.
Writing solution file op_00000.dat.
Iteration: 10 Time: 4.000E-02 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5129E-02 Conservation loss: 1.7023E-16
Writing solution file advection_field_00001.dat.
Writing solution file op_00001.dat.
Iteration: 20 Time: 8.000E-02 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5129E-02 Conservation loss: 3.8015E-18
Writing solution file advection_field_00002.dat.
Writing solution file op_00002.dat.
Iteration: 30 Time: 1.200E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5129E-02 Conservation loss: 2.8630E-17
Writing solution file advection_field_00003.dat.
Writing solution file op_00003.dat.
Iteration: 40 Time: 1.600E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5128E-02 Conservation loss: 1.0875E-16
Writing solution file advection_field_00004.dat.
Writing solution file op_00004.dat.
Iteration: 50 Time: 2.000E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5127E-02 Conservation loss: 2.0041E-16
Writing solution file advection_field_00005.dat.
Writing solution file op_00005.dat.
Iteration: 60 Time: 2.400E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5152E-02 Conservation loss: 7.0344E-17
Writing solution file advection_field_00006.dat.
Writing solution file op_00006.dat.
Iteration: 70 Time: 2.800E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4968E-02 Conservation loss: 2.5072E-18
Writing solution file advection_field_00007.dat.
Writing solution file op_00007.dat.
Iteration: 80 Time: 3.200E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4901E-02 Conservation loss: 1.5736E-16
Writing solution file advection_field_00008.dat.
Writing solution file op_00008.dat.
Iteration: 90 Time: 3.600E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4909E-02 Conservation loss: 4.7068E-17
Writing solution file advection_field_00009.dat.
Writing solution file op_00009.dat.
Iteration: 100 Time: 4.000E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4755E-02 Conservation loss: 9.4990E-17
Writing solution file advection_field_00010.dat.
Writing solution file op_00010.dat.
Iteration: 110 Time: 4.400E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4580E-02 Conservation loss: 1.6137E-16
Writing solution file advection_field_00011.dat.
Writing solution file op_00011.dat.
Iteration: 120 Time: 4.800E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4271E-02 Conservation loss: 3.2906E-17
Writing solution file advection_field_00012.dat.
Writing solution file op_00012.dat.
Iteration: 130 Time: 5.200E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4041E-02 Conservation loss: 8.4991E-17
Writing solution file advection_field_00013.dat.
Writing solution file op_00013.dat.
Iteration: 140 Time: 5.600E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4207E-02 Conservation loss: 5.0991E-18
Writing solution file advection_field_00014.dat.
Writing solution file op_00014.dat.
Iteration: 150 Time: 6.000E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4005E-02 Conservation loss: 4.0322E-17
Writing solution file advection_field_00015.dat.
Writing solution file op_00015.dat.
Iteration: 160 Time: 6.400E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.3847E-02 Conservation loss: 4.0312E-17
Writing solution file advection_field_00016.dat.
Writing solution file op_00016.dat.
Iteration: 170 Time: 6.800E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.3615E-02 Conservation loss: 1.2268E-16
Writing solution file advection_field_00017.dat.
Writing solution file op_00017.dat.
Iteration: 180 Time: 7.200E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.3670E-02 Conservation loss: 5.3397E-17
Writing solution file advection_field_00018.dat.
Writing solution file op_00018.dat.
Iteration: 190 Time: 7.600E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.3562E-02 Conservation loss: 7.0683E-17
Writing solution file advection_field_00019.dat.
Writing solution file op_00019.dat.
Iteration: 200 Time: 8.000E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.2839E-02 Conservation loss: 7.4121E-17
Writing solution file advection_field_00020.dat.
Writing solution file op_00020.dat.
Iteration: 210 Time: 8.400E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.3312E-02 Conservation loss: 8.8922E-17
Writing solution file advection_field_00021.dat.
Writing solution file op_00021.dat.
Iteration: 220 Time: 8.800E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.1960E-02 Conservation loss: 3.3567E-17
Writing solution file advection_field_00022.dat.
Writing solution file op_00022.dat.
Iteration: 230 Time: 9.200E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.1649E-02 Conservation loss: 5.7708E-18
Writing solution file advection_field_00023.dat.
Writing solution file op_00023.dat.
Iteration: 240 Time: 9.600E-01 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.1281E-02 Conservation loss: 1.0526E-16
Writing solution file advection_field_00024.dat.
Writing solution file op_00024.dat.
Iteration: 250 Time: 1.000E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.0912E-02 Conservation loss: 4.9737E-17
Writing solution file advection_field_00025.dat.
Writing solution file op_00025.dat.
Iteration: 260 Time: 1.040E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.0821E-02 Conservation loss: 2.3658E-18
Writing solution file advection_field_00026.dat.
Writing solution file op_00026.dat.
Iteration: 270 Time: 1.080E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.0245E-02 Conservation loss: 1.0698E-18
Writing solution file advection_field_00027.dat.
Writing solution file op_00027.dat.
Iteration: 280 Time: 1.120E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.9980E-02 Conservation loss: 4.4055E-17
Writing solution file advection_field_00028.dat.
Writing solution file op_00028.dat.
Iteration: 290 Time: 1.160E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.9316E-02 Conservation loss: 4.6110E-17
Writing solution file advection_field_00029.dat.
Writing solution file op_00029.dat.
Iteration: 300 Time: 1.200E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.8337E-02 Conservation loss: 4.0633E-17
Writing solution file advection_field_00030.dat.
Writing solution file op_00030.dat.
Iteration: 310 Time: 1.240E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.7183E-02 Conservation loss: 8.4233E-17
Writing solution file advection_field_00031.dat.
Writing solution file op_00031.dat.
Iteration: 320 Time: 1.280E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.5925E-02 Conservation loss: 1.2881E-17
Writing solution file advection_field_00032.dat.
Writing solution file op_00032.dat.
Iteration: 330 Time: 1.320E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.5325E-02 Conservation loss: 6.0131E-18
Writing solution file advection_field_00033.dat.
Writing solution file op_00033.dat.
Iteration: 340 Time: 1.360E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.4249E-02 Conservation loss: 8.1739E-19
Writing solution file advection_field_00034.dat.
Writing solution file op_00034.dat.
Iteration: 350 Time: 1.400E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.3376E-02 Conservation loss: 3.7448E-17
Writing solution file advection_field_00035.dat.
Writing solution file op_00035.dat.
Iteration: 360 Time: 1.440E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.2835E-02 Conservation loss: 4.2665E-18
Writing solution file advection_field_00036.dat.
Writing solution file op_00036.dat.
Iteration: 370 Time: 1.480E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.1837E-02 Conservation loss: 7.0223E-17
Writing solution file advection_field_00037.dat.
Writing solution file op_00037.dat.
Iteration: 380 Time: 1.520E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.1116E-02 Conservation loss: 3.5537E-17
Writing solution file advection_field_00038.dat.
Writing solution file op_00038.dat.
Iteration: 390 Time: 1.560E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.0688E-02 Conservation loss: 5.6364E-17
Writing solution file advection_field_00039.dat.
Writing solution file op_00039.dat.
Iteration: 400 Time: 1.600E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 9.8700E-03 Conservation loss: 1.9859E-16
Writing solution file advection_field_00040.dat.
Writing solution file op_00040.dat.
Iteration: 410 Time: 1.640E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 9.1846E-03 Conservation loss: 7.3728E-17
Writing solution file advection_field_00041.dat.
Writing solution file op_00041.dat.
Iteration: 420 Time: 1.680E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 8.7721E-03 Conservation loss: 9.5147E-18
Writing solution file advection_field_00042.dat.
Writing solution file op_00042.dat.
Iteration: 430 Time: 1.720E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 8.0586E-03 Conservation loss: 8.2409E-17
Writing solution file advection_field_00043.dat.
Writing solution file op_00043.dat.
Iteration: 440 Time: 1.760E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 7.6601E-03 Conservation loss: 1.5004E-16
Writing solution file advection_field_00044.dat.
Writing solution file op_00044.dat.
Iteration: 450 Time: 1.800E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 7.1324E-03 Conservation loss: 1.1875E-16
Writing solution file advection_field_00045.dat.
Writing solution file op_00045.dat.
Iteration: 460 Time: 1.840E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.5630E-03 Conservation loss: 1.2223E-16
Writing solution file advection_field_00046.dat.
Writing solution file op_00046.dat.
Iteration: 470 Time: 1.880E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.2473E-03 Conservation loss: 5.4750E-17
Writing solution file advection_field_00047.dat.
Writing solution file op_00047.dat.
Iteration: 480 Time: 1.920E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 5.6273E-03 Conservation loss: 1.3608E-16
Writing solution file advection_field_00048.dat.
Writing solution file op_00048.dat.
Iteration: 490 Time: 1.960E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 5.3640E-03 Conservation loss: 1.4636E-17
Writing solution file advection_field_00049.dat.
Writing solution file op_00049.dat.
Iteration: 500 Time: 2.000E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 4.9294E-03 Conservation loss: 7.7086E-17
Writing solution file advection_field_00050.dat.
Writing solution file op_00050.dat.
Iteration: 510 Time: 2.040E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 4.5437E-03 Conservation loss: 3.8981E-17
Writing solution file advection_field_00051.dat.
Writing solution file op_00051.dat.
Iteration: 520 Time: 2.080E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 4.1907E-03 Conservation loss: 4.5949E-17
Writing solution file advection_field_00052.dat.
Writing solution file op_00052.dat.
Iteration: 530 Time: 2.120E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 3.9753E-03 Conservation loss: 3.3736E-16
Writing solution file advection_field_00053.dat.
Writing solution file op_00053.dat.
Iteration: 540 Time: 2.160E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 3.7346E-03 Conservation loss: 7.0223E-17
Writing solution file advection_field_00054.dat.
Writing solution file op_00054.dat.
Iteration: 550 Time: 2.200E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 3.4860E-03 Conservation loss: 2.5159E-17
Writing solution file advection_field_00055.dat.
Writing solution file op_00055.dat.
Iteration: 560 Time: 2.240E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 3.2570E-03 Conservation loss: 1.1539E-16
Writing solution file advection_field_00056.dat.
Writing solution file op_00056.dat.
Iteration: 570 Time: 2.280E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 3.0597E-03 Conservation loss: 5.4604E-17
Writing solution file advection_field_00057.dat.
Writing solution file op_00057.dat.
Iteration: 580 Time: 2.320E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.9081E-03 Conservation loss: 1.1191E-16
Writing solution file advection_field_00058.dat.
Writing solution file op_00058.dat.
Iteration: 590 Time: 2.360E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.7664E-03 Conservation loss: 9.1084E-17
Writing solution file advection_field_00059.dat.
Writing solution file op_00059.dat.
Iteration: 600 Time: 2.400E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.5890E-03 Conservation loss: 4.9437E-17
Writing solution file advection_field_00060.dat.
Writing solution file op_00060.dat.
Iteration: 610 Time: 2.440E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.4468E-03 Conservation loss: 4.7674E-17
Writing solution file advection_field_00061.dat.
Writing solution file op_00061.dat.
Iteration: 620 Time: 2.480E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.2984E-03 Conservation loss: 4.9496E-17
Writing solution file advection_field_00062.dat.
Writing solution file op_00062.dat.
Iteration: 630 Time: 2.520E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.1890E-03 Conservation loss: 2.3336E-16
Writing solution file advection_field_00063.dat.
Writing solution file op_00063.dat.
Iteration: 640 Time: 2.560E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 2.0905E-03 Conservation loss: 4.2507E-17
Writing solution file advection_field_00064.dat.
Writing solution file op_00064.dat.
Iteration: 650 Time: 2.600E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.9949E-03 Conservation loss: 3.2071E-17
Writing solution file advection_field_00065.dat.
Writing solution file op_00065.dat.
Iteration: 660 Time: 2.640E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.8992E-03 Conservation loss: 9.8006E-17
Writing solution file advection_field_00066.dat.
Writing solution file op_00066.dat.
Iteration: 670 Time: 2.680E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.8046E-03 Conservation loss: 4.2488E-17
Writing solution file advection_field_00067.dat.
Writing solution file op_00067.dat.
Iteration: 680 Time: 2.720E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.7113E-03 Conservation loss: 2.3428E-17
Writing solution file advection_field_00068.dat.
Writing solution file op_00068.dat.
Iteration: 690 Time: 2.760E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.6250E-03 Conservation loss: 4.0785E-17
Writing solution file advection_field_00069.dat.
Writing solution file op_00069.dat.
Iteration: 700 Time: 2.800E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.5570E-03 Conservation loss: 4.7724E-17
Writing solution file advection_field_00070.dat.
Writing solution file op_00070.dat.
Iteration: 710 Time: 2.840E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.4964E-03 Conservation loss: 1.6487E-17
Writing solution file advection_field_00071.dat.
Writing solution file op_00071.dat.
Iteration: 720 Time: 2.880E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.4492E-03 Conservation loss: 1.0146E-16
Writing solution file advection_field_00072.dat.
Writing solution file op_00072.dat.
Iteration: 730 Time: 2.920E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.3971E-03 Conservation loss: 9.1047E-17
Writing solution file advection_field_00073.dat.
Writing solution file op_00073.dat.
Iteration: 740 Time: 2.960E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.3322E-03 Conservation loss: 6.6791E-17
Writing solution file advection_field_00074.dat.
Writing solution file op_00074.dat.
Iteration: 750 Time: 3.000E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.2806E-03 Conservation loss: 1.6450E-17
Writing solution file advection_field_00075.dat.
Writing solution file op_00075.dat.
Iteration: 760 Time: 3.040E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.2328E-03 Conservation loss: 2.1601E-16
Writing solution file advection_field_00076.dat.
Writing solution file op_00076.dat.
Iteration: 770 Time: 3.080E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.1718E-03 Conservation loss: 2.4377E-16
Writing solution file advection_field_00077.dat.
Writing solution file op_00077.dat.
Iteration: 780 Time: 3.120E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.1218E-03 Conservation loss: 6.3378E-17
Writing solution file advection_field_00078.dat.
Writing solution file op_00078.dat.
Iteration: 790 Time: 3.160E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.0835E-03 Conservation loss: 1.3278E-16
Writing solution file advection_field_00079.dat.
Writing solution file op_00079.dat.
Iteration: 800 Time: 3.200E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.0494E-03 Conservation loss: 6.1529E-17
Writing solution file advection_field_00080.dat.
Writing solution file op_00080.dat.
Iteration: 810 Time: 3.240E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 1.0079E-03 Conservation loss: 9.4575E-17
Writing solution file advection_field_00081.dat.
Writing solution file op_00081.dat.
Iteration: 820 Time: 3.280E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 9.6777E-04 Conservation loss: 8.0740E-17
Writing solution file advection_field_00082.dat.
Writing solution file op_00082.dat.
Iteration: 830 Time: 3.320E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 9.3024E-04 Conservation loss: 1.2931E-16
Writing solution file advection_field_00083.dat.
Writing solution file op_00083.dat.
Iteration: 840 Time: 3.360E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 8.9180E-04 Conservation loss: 1.2582E-16
Writing solution file advection_field_00084.dat.
Writing solution file op_00084.dat.
Iteration: 850 Time: 3.400E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 8.6813E-04 Conservation loss: 4.2574E-17
Writing solution file advection_field_00085.dat.
Writing solution file op_00085.dat.
Iteration: 860 Time: 3.440E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 8.3445E-04 Conservation loss: 5.1082E-17
Writing solution file advection_field_00086.dat.
Writing solution file op_00086.dat.
Iteration: 870 Time: 3.480E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 8.1592E-04 Conservation loss: 6.3359E-17
Writing solution file advection_field_00087.dat.
Writing solution file op_00087.dat.
Iteration: 880 Time: 3.520E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 7.8870E-04 Conservation loss: 1.4773E-17
Writing solution file advection_field_00088.dat.
Writing solution file op_00088.dat.
Iteration: 890 Time: 3.560E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 7.7119E-04 Conservation loss: 8.7638E-17
Writing solution file advection_field_00089.dat.
Writing solution file op_00089.dat.
Iteration: 900 Time: 3.600E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 7.4693E-04 Conservation loss: 7.8495E-18
Writing solution file advection_field_00090.dat.
Writing solution file op_00090.dat.
Iteration: 910 Time: 3.640E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 7.2381E-04 Conservation loss: 1.2232E-16
Writing solution file advection_field_00091.dat.
Writing solution file op_00091.dat.
Iteration: 920 Time: 3.680E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.9578E-04 Conservation loss: 4.4147E-17
Writing solution file advection_field_00092.dat.
Writing solution file op_00092.dat.
Iteration: 930 Time: 3.720E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.7511E-04 Conservation loss: 4.9517E-17
Writing solution file advection_field_00093.dat.
Writing solution file op_00093.dat.
Iteration: 940 Time: 3.760E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.5964E-04 Conservation loss: 7.8846E-17
Writing solution file advection_field_00094.dat.
Writing solution file op_00094.dat.
Iteration: 950 Time: 3.800E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.5050E-04 Conservation loss: 4.6049E-17
Writing solution file advection_field_00095.dat.
Writing solution file op_00095.dat.
Iteration: 960 Time: 3.840E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.4648E-04 Conservation loss: 1.6402E-16
Writing solution file advection_field_00096.dat.
Writing solution file op_00096.dat.
Iteration: 970 Time: 3.880E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.2871E-04 Conservation loss: 1.2392E-16
Writing solution file advection_field_00097.dat.
Writing solution file op_00097.dat.
Iteration: 980 Time: 3.920E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 6.1416E-04 Conservation loss: 5.3010E-17
Writing solution file advection_field_00098.dat.
Writing solution file op_00098.dat.
Iteration: 990 Time: 3.960E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 5.9852E-04 Conservation loss: 7.7279E-17
Writing solution file advection_field_00099.dat.
Writing solution file op_00099.dat.
Iteration: 1000 Time: 4.000E+00 Max CFL: 5.120E-01 Max Diff. No.: 0.000E+00 Norm: 5.6142E-04 Conservation loss: 5.6469E-17
Writing solution file advection_field_00100.dat.
Writing solution file op_00100.dat.
Completed time integration (Final time: 4.000000).
Computed errors for domain 0:
L1 Error : 0.0000000000000000E+00
L2 Error : 0.0000000000000000E+00
Linfinity Error : 0.0000000000000000E+00
Conservation Errors:
5.6469145494602441E-17
Solver runtime (in seconds): 2.0189999000000000E+01
Total runtime (in seconds): 2.0231522999999999E+01
Deallocating arrays.
Finished.