3D Linear Advection - Gaussian Pulse
Location: hypar/Examples/3D/LinearAdvection/GaussianPulse (This directory contains all the input files needed to run this case. If there is a Run.m, run it in MATLAB to quickly set up, run, and visualize the example).
Governing equations: 3D Linear Advection Equation (linearadr.h)
Domain: \(-3 \le x,y,z < 3\), "periodic" (_PERIODIC_) boundary conditions on all boundaries.
Initial solution: \(u\left(x,y,0\right) = u_0\left(x,y\right)= \exp\left[-\left(\frac{x^2}{2}+\frac{y^2}{2}+\frac{z^2}{2}\right)\right]\)
Exact solution: \(u\left(x,y,t\right) = u_0\left(x-a_xt,y-a_yt,z-a_zt\right)\).
Numerical Method:
- Spatial discretization (hyperbolic): 5th order CRWENO (Interp1PrimFifthOrderCRWENO())
- Time integration: RK4 (TimeRK(), _RK_44_)
Input files required:
solver.inp
begin
ndims 3
nvars 1
size 64 64 64
iproc 2 2 2
ghost 3
n_iter 120
time_scheme rk
time_scheme_type 44
hyp_space_scheme crweno5
conservation_check yes
dt 0.05
screen_op_iter 1
file_op_iter 12
ip_file_type binary
input_mode serial
op_file_format binary
output_mode serial
op_overwrite no
model linear-advection-diffusion-reaction
end
boundary.inp
6
periodic 0 1 0 0 -3.0 3.0 -3.0 3.0
periodic 0 -1 0 0 -3.0 3.0 -3.0 3.0
periodic 1 1 -3.0 3.0 0 0 -3.0 3.0
periodic 1 -1 -3.0 3.0 0 0 -3.0 3.0
periodic 2 1 -3.0 3.0 -3.0 3.0 0 0
periodic 2 -1 -3.0 3.0 -3.0 3.0 0 0
physics.inp (specifies \(a_x\), \(a_y\), and \(a_z\))
begin
advection 1.0 0.0 0.0
end
lusolver.inp (optional)
begin
reducedsolvetype jacobi
evaluate_norm 0
maxiter 4
atol 1e-12
rtol 1e-10
verbose 0
end
weno.inp (optional)
begin
mapped 1
borges 0
yc 0
no_limiting 0
epsilon 0.000001
p 2.0
rc 0.3
xi 0.001
end
To generate initial.inp, compile and run the following code in the run directory. Note: if the final time is an integer multiple of the time period, the file initial.inp can also be used as the exact solution exact.inp (i.e. create a sym link called exact.inp pointing to initial.inp, or just copy initial.inp to exact.inp).
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
int main()
{
int NI=64,NJ=64,NK=64,ndims=3;
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) printf("Error: Input file \"solver.inp\" not found. Default values will be used.\n");
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");
}
fclose(in);
if (ndims != 3) {
printf("ndims is not 3 in solver.inp. this code is to generate 3D initial conditions\n");
return(0);
}
printf("Grid:\t\t\t%d X %d X %d\n",NI,NJ,NK);
int i,j,k;
double dx = 12.0 / ((double)NI);
double dy = 6.0 / ((double)NJ);
double dz = 6.0 / ((double)NK);
double *x, *y, *z, *u;
x = (double*) calloc (NI , sizeof(double));
y = (double*) calloc (NJ , sizeof(double));
z = (double*) calloc (NK , sizeof(double));
u = (double*) calloc (NI*NJ*NK, sizeof(double));
for (i = 0; i < NI; i++){
for (j = 0; j < NJ; j++){
for (k = 0; k < NK; k++) {
x[i] = -6 + i*dx;
y[j] = -3 + j*dy;
z[k] = -3 + k*dz;
int p = i + NI*j + NI*NJ*k;
u[p] = exp(-((x[i]*x[i]/2+y[j]*y[j]/2+z[k]*z[k]/2)));
}
}
}
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,"%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[p]);
}
}
}
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),NI*NJ*NK,out);
fclose(out);
}
free(x);
free(y);
free(z);
free(u);
return(0);
}
Output:
Note that iproc is set to
2 2 2
in solver.inp (i.e., 2 processors along x, y, and z). Thus, this example should be run with 8 MPI ranks (or change iproc).
After running the code, there should be 11 output files op_00000.bin, op_00001.bin, ... op_00010.bin; the first one is the solution at \(t=0\) and the final one is the solution at \(t=6\). Since HyPar::op_overwrite is set to no in solver.inp, separate files are written for solutions at each output time.
All the files are binary (HyPar::op_file_format is set to binary in solver.inp). The code hypar/Extras/BinaryToTecplot.c can be used to convert the binary solution files to 3D Tecplot files that can be visualized in any software supporting the Tecplot format. Similarly, the code hypar/Extras/BinaryToText.c can be used to convert the binary solution files to ASCII text files with the following data layout: the first three columns are grid indices, the next three columns are x, y, and z coordinates, and the last column is the solution u.
The following animation was generated from the solution files (after converting to Tecplot format and plotting the iso-surface in VisIt):
Since the exact solution is available at the final time (exact.inp is a copy of initial.inp), the numerical errors are calculated and reported on screen (see below) as well as errors.dat:
64 64 64 2 2 2 5.0000000000000003E-02 1.5281299296958855E-04 4.0481589826766229E-04 1.4642373010287230E-03 5.7936165000000003E+01 5.7977089999999997E+01
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 errors (HyPar::error), solver wall time (seconds) (i.e., not accounting for initialization, and cleaning up), and total wall time.
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:
64 64 64 2 2 2 5.0000000000000003E-02 1.3759209333992338E-14
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 8 processes
Reading solver inputs from file "solver.inp".
No. of dimensions : 3
No. of variables : 1
Domain size : 64 64 64
Processes along each dimension : 2 2 2
No. of ghosts pts : 3
No. of iter. : 120
Restart iteration : 0
Time integration scheme : rk (44)
Spatial discretization scheme (hyperbolic) : crweno5
Split hyperbolic flux term? : no
Interpolation type for hyperbolic term : characteristic
Spatial discretization type (parabolic ) : nonconservative-1stage
Spatial discretization scheme (parabolic ) : 2
Time Step : 5.000000E-02
Check for conservation : yes
Screen output iterations : 1
File output iterations : 12
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 : 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: 1.5621477393793244E+01
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
Boundary periodic: Along dimension 2 and face +1
Boundary periodic: Along dimension 2 and face -1
6 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".
Setting up time integration.
Solving in time (from 0 to 120 iterations)
Writing solution file op_00000.bin.
Iteration: 1 Time: 5.000E-02 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6743E-03 Conservation loss: 9.4381E-15
Iteration: 2 Time: 1.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6743E-03 Conservation loss: 1.3532E-14
Iteration: 3 Time: 1.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6743E-03 Conservation loss: 5.2308E-15
Iteration: 4 Time: 2.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6743E-03 Conservation loss: 1.2167E-14
Iteration: 5 Time: 2.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6743E-03 Conservation loss: 7.2776E-15
Iteration: 6 Time: 3.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.0575E-14
Iteration: 7 Time: 3.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 3.8662E-15
Iteration: 8 Time: 4.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 5.5719E-15
Iteration: 9 Time: 4.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 3.2977E-15
Iteration: 10 Time: 5.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.0689E-14
Iteration: 11 Time: 5.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 3.2977E-15
Iteration: 12 Time: 6.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.2167E-14
Writing solution file op_00001.bin.
Iteration: 13 Time: 6.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 6.3679E-15
Iteration: 14 Time: 7.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 8.3010E-15
Iteration: 15 Time: 7.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.1030E-14
Iteration: 16 Time: 8.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.2395E-14
Iteration: 17 Time: 8.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.0120E-14
Iteration: 18 Time: 9.000E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 5.1171E-15
Iteration: 19 Time: 9.500E-01 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 5.3445E-15
Iteration: 20 Time: 1.000E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 8.3010E-15
Iteration: 21 Time: 1.050E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.6033E-14
Iteration: 22 Time: 1.100E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.8876E-14
Iteration: 23 Time: 1.150E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 2.0355E-14
Iteration: 24 Time: 1.200E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.0575E-14
Writing solution file op_00002.bin.
Iteration: 25 Time: 1.250E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 4.6622E-15
Iteration: 26 Time: 1.300E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.1144E-14
Iteration: 27 Time: 1.350E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.2622E-14
Iteration: 28 Time: 1.400E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 9.8930E-15
Iteration: 29 Time: 1.450E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 8.0736E-15
Iteration: 30 Time: 1.500E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 8.7559E-15
Iteration: 31 Time: 1.550E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 6.0268E-15
Iteration: 32 Time: 1.600E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.1599E-14
Iteration: 33 Time: 1.650E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 6.8227E-16
Iteration: 34 Time: 1.700E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6742E-03 Conservation loss: 1.3759E-14
Iteration: 35 Time: 1.750E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.3913E-15
Iteration: 36 Time: 1.800E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 4.6622E-15
Writing solution file op_00003.bin.
Iteration: 37 Time: 1.850E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.2308E-15
Iteration: 38 Time: 1.900E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1826E-14
Iteration: 39 Time: 1.950E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1030E-14
Iteration: 40 Time: 2.000E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.7993E-15
Iteration: 41 Time: 2.050E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.1639E-15
Iteration: 42 Time: 2.100E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.3010E-15
Iteration: 43 Time: 2.150E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.0575E-14
Iteration: 44 Time: 2.200E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1371E-16
Iteration: 45 Time: 2.250E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.5719E-15
Iteration: 46 Time: 2.300E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.5806E-14
Iteration: 47 Time: 2.350E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.6856E-16
Iteration: 48 Time: 2.400E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.6187E-15
Writing solution file op_00004.bin.
Iteration: 49 Time: 2.450E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 4.4348E-15
Iteration: 50 Time: 2.500E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.9833E-15
Iteration: 51 Time: 2.550E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.9331E-15
Iteration: 52 Time: 2.600E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.8462E-15
Iteration: 53 Time: 2.650E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1712E-14
Iteration: 54 Time: 2.700E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 3.2977E-15
Iteration: 55 Time: 2.750E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.8462E-15
Iteration: 56 Time: 2.800E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.6656E-15
Iteration: 57 Time: 2.850E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.3010E-15
Iteration: 58 Time: 2.900E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.7324E-15
Iteration: 59 Time: 2.950E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.5719E-15
Iteration: 60 Time: 3.000E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 6.5953E-15
Writing solution file op_00005.bin.
Iteration: 61 Time: 3.050E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 4.3211E-15
Iteration: 62 Time: 3.100E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 2.3880E-15
Iteration: 63 Time: 3.150E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.1639E-15
Iteration: 64 Time: 3.200E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.0348E-14
Iteration: 65 Time: 3.250E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.9599E-16
Iteration: 66 Time: 3.300E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.4147E-15
Iteration: 67 Time: 3.350E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.2107E-15
Iteration: 68 Time: 3.400E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.9331E-15
Iteration: 69 Time: 3.450E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1258E-14
Iteration: 70 Time: 3.500E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1485E-14
Iteration: 71 Time: 3.550E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 2.2742E-15
Iteration: 72 Time: 3.600E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.5124E-14
Writing solution file op_00006.bin.
Iteration: 73 Time: 3.650E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.3445E-15
Iteration: 74 Time: 3.700E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.3759E-14
Iteration: 75 Time: 3.750E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.1171E-15
Iteration: 76 Time: 3.800E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 3.8662E-15
Iteration: 77 Time: 3.850E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.1639E-15
Iteration: 78 Time: 3.900E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.7171E-14
Iteration: 79 Time: 3.950E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.9833E-15
Iteration: 80 Time: 4.000E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.6033E-14
Iteration: 81 Time: 4.050E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.8930E-15
Iteration: 82 Time: 4.100E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.7739E-14
Iteration: 83 Time: 4.150E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.4381E-15
Iteration: 84 Time: 4.200E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.0803E-14
Writing solution file op_00007.bin.
Iteration: 85 Time: 4.250E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.5284E-15
Iteration: 86 Time: 4.300E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.9833E-15
Iteration: 87 Time: 4.350E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.4100E-14
Iteration: 88 Time: 4.400E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.2736E-14
Iteration: 89 Time: 4.450E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.8462E-15
Iteration: 90 Time: 4.500E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.4381E-15
Iteration: 91 Time: 4.550E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.0120E-14
Iteration: 92 Time: 4.600E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.0575E-14
Iteration: 93 Time: 4.650E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 5.6856E-16
Iteration: 94 Time: 4.700E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.2107E-15
Iteration: 95 Time: 4.750E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.5284E-15
Iteration: 96 Time: 4.800E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.3244E-15
Writing solution file op_00008.bin.
Iteration: 97 Time: 4.850E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.3191E-14
Iteration: 98 Time: 4.900E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 6.9365E-15
Iteration: 99 Time: 4.950E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.2508E-14
Iteration: 100 Time: 5.000E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 3.1839E-15
Iteration: 101 Time: 5.050E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 3.2977E-15
Iteration: 102 Time: 5.100E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.6829E-14
Iteration: 103 Time: 5.150E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.2107E-15
Iteration: 104 Time: 5.200E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.6716E-14
Iteration: 105 Time: 5.250E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.8462E-15
Iteration: 106 Time: 5.300E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1371E-15
Iteration: 107 Time: 5.350E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.2776E-15
Iteration: 108 Time: 5.400E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.1599E-14
Writing solution file op_00009.bin.
Iteration: 109 Time: 5.450E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.3077E-14
Iteration: 110 Time: 5.500E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.0348E-14
Iteration: 111 Time: 5.550E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.3987E-14
Iteration: 112 Time: 5.600E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 7.2776E-15
Iteration: 113 Time: 5.650E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 9.8930E-15
Iteration: 114 Time: 5.700E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 4.8896E-15
Iteration: 115 Time: 5.750E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.6421E-15
Iteration: 116 Time: 5.800E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.6375E-14
Iteration: 117 Time: 5.850E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.5284E-15
Iteration: 118 Time: 5.900E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 6.8227E-15
Iteration: 119 Time: 5.950E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 8.5284E-15
Iteration: 120 Time: 6.000E+00 Max CFL: 5.333E-01 Max Diff. No.: 0.000E+00 Norm: 5.6741E-03 Conservation loss: 1.3759E-14
Writing solution file op_00010.bin.
Completed time integration (Final time: 6.000000).
Reading array from binary file exact.inp (Serial mode).
Computed errors:
L1 Error : 1.5281299296958855E-04
L2 Error : 4.0481589826766229E-04
Linfinity Error : 1.4642373010287230E-03
Conservation Errors:
1.3759209333992338E-14
Solver runtime (in seconds): 5.7936165000000003E+01
Total runtime (in seconds): 5.7977089999999997E+01
Deallocating arrays.
Finished.