1D Linear Advection - Sine Wave with Spatially-Varying Advection Speed
Location: Examples/1D/LinearAdvection/SineWave_NonConstantAdvection (This directory contains all the input files needed to run this case.)
Governing equations: 1D Linear Advection Equation (linearadr.h)
Domain: \(0 \le x < 1\), "periodic" (_PERIODIC_) boundary conditions
Initial solution: \(u\left(x,0\right) = \sin\left(2\pi x\right)\)
Advection speed: \(a\left(x\right) = 1 + \frac{1}{2}\sin^2\left(2\pi x\right)\)
Numerical Method:
- Spatial discretization (hyperbolic): 5th order WENO (Interp1PrimFifthOrderWENO())
- Time integration: RK4 (TimeRK(), _RK_44_)
Input files required:
solver.inp
begin
ndims 1
nvars 1
size 80
iproc 1
ghost 3
n_iter 1000
time_scheme rk
time_scheme_type 44
hyp_space_scheme weno5
conservation_check yes
dt 0.0025
screen_op_iter 10
file_op_iter 10
ip_file_type ascii
op_file_format text
op_overwrite no
model linear-advection-diffusion-reaction
end
boundary.inp
2
periodic 0 1 0 0
periodic 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.
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 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, 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) {
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);
} 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);
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;
}
if (ndims != 1) {
printf("ndims is not 1 in solver.inp. this code is to generate 1D initial conditions\n");
return(0);
}
printf("Grid:\t\t\t%d\n",NI);
int i;
double dx = 1.0 / ((double)NI);
double *x, *u, *a;
x = (double*) calloc (NI, sizeof(double));
u = (double*) calloc (NI, sizeof(double));
a = (double*) calloc (NI, sizeof(double));
for (i = 0; i < NI; i++){
x[i] = (i+0.5)*dx;
u[i] = sin(2*pi*x[i]);
a[i] = 1.0+0.5*sin(2*pi*x[i])*sin(2*pi*x[i]);
}
FILE *out;
strcat(adv_filename, ".inp");
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 (i = 0; i < NI; i++) fprintf(out,"%lf ",u[i]);
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,"%1.16E ",x[i]);
fprintf(out,"\n");
for (i = 0; i < NI; i++) fprintf(out,"%1.16E ",a[i]);
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(u,sizeof(double),NI,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(a,sizeof(double),NI,out);
fclose(out);
}
free(x);
free(u);
free(a);
return(0);
}
Output:
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 \(t=2.5\). 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 ASCII text (HyPar::op_file_format is set to text in solver.inp). In these files, the first column is grid index, the second column is x-coordinate, and the third column is the solution.
The following animation shows the solution vs. grid point index:
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 \(a\left(x\right)\). The following figure shows the advection speed vs. grid point index:
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:
80 1 2.5000000000000001E-03 1.5048726154098802E-16
The numbers are: number of grid points (HyPar::dim_global), number of processors (MPIVariables::iproc), time step size (HyPar::dt), and conservation error (HyPar::ConservationError).
Expected screen output:
HyPar - Parallel (MPI) version with 1 processes
Compiled with PETSc time integration.
Allocated simulation object(s).
Reading solver inputs from file "solver.inp".
No. of dimensions : 1
No. of variables : 1
Domain size : 80
Processes along each dimension : 1
No. of ghosts pts : 3
No. of iter. : 1000
Restart iteration : 0
Time integration scheme : rk (44)
Spatial discretization scheme (hyperbolic) : weno5
Split hyperbolic flux term? : no
Interpolation type for hyperbolic term : characteristic
Spatial discretization type (parabolic ) : nonconservative-1stage
Spatial discretization scheme (parabolic ) : 2
Time Step : 2.500000E-03
Check for conservation : yes
Screen output iterations : 10
File output iterations : 10
Initial solution file type : ascii
Initial solution read mode : serial
Solution file write mode : serial
Solution file format : text
Overwrite solution file : no
Physical model : linear-advection-diffusion-reaction
Partitioning domain.
Allocating data arrays.
Reading array from ASCII file initial.inp (Serial mode).
Volume integral of the initial solution:
0: 4.9005938196344800E-17
Reading boundary conditions from boundary.inp.
Boundary periodic: Along dimension 0 and face +1
Boundary periodic: Along dimension 0 and face -1
2 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 ASCII 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: 2.500E-02 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5828E-02 Conservation loss: 8.4134E-17
Writing solution file advection_field_00001.dat.
Writing solution file op_00001.dat.
Iteration: 20 Time: 5.000E-02 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5825E-02 Conservation loss: 4.0332E-17
Writing solution file advection_field_00002.dat.
Writing solution file op_00002.dat.
Iteration: 30 Time: 7.500E-02 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5819E-02 Conservation loss: 3.1659E-17
Writing solution file advection_field_00003.dat.
Writing solution file op_00003.dat.
Iteration: 40 Time: 1.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5811E-02 Conservation loss: 1.5179E-17
Writing solution file advection_field_00004.dat.
Writing solution file op_00004.dat.
Iteration: 50 Time: 1.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5804E-02 Conservation loss: 5.0741E-17
Writing solution file advection_field_00005.dat.
Writing solution file op_00005.dat.
Iteration: 60 Time: 1.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5798E-02 Conservation loss: 8.0231E-17
Writing solution file advection_field_00006.dat.
Writing solution file op_00006.dat.
Iteration: 70 Time: 1.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5793E-02 Conservation loss: 7.3726E-18
Writing solution file advection_field_00007.dat.
Writing solution file op_00007.dat.
Iteration: 80 Time: 2.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5791E-02 Conservation loss: 8.0231E-17
Writing solution file advection_field_00008.dat.
Writing solution file op_00008.dat.
Iteration: 90 Time: 2.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5792E-02 Conservation loss: 2.3852E-17
Writing solution file advection_field_00009.dat.
Writing solution file op_00009.dat.
Iteration: 100 Time: 2.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5795E-02 Conservation loss: 4.6404E-17
Writing solution file advection_field_00010.dat.
Writing solution file op_00010.dat.
Iteration: 110 Time: 2.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5801E-02 Conservation loss: 6.9823E-17
Writing solution file advection_field_00011.dat.
Writing solution file op_00011.dat.
Iteration: 120 Time: 3.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5808E-02 Conservation loss: 4.8139E-17
Writing solution file advection_field_00012.dat.
Writing solution file op_00012.dat.
Iteration: 130 Time: 3.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5815E-02 Conservation loss: 1.9212E-16
Writing solution file advection_field_00013.dat.
Writing solution file op_00013.dat.
Iteration: 140 Time: 3.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5822E-02 Conservation loss: 4.5536E-17
Writing solution file advection_field_00014.dat.
Writing solution file op_00014.dat.
Iteration: 150 Time: 3.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 2.6021E-17
Writing solution file advection_field_00015.dat.
Writing solution file op_00015.dat.
Iteration: 160 Time: 4.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5829E-02 Conservation loss: 1.6209E-16
Writing solution file advection_field_00016.dat.
Writing solution file op_00016.dat.
Iteration: 170 Time: 4.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5829E-02 Conservation loss: 1.7434E-16
Writing solution file advection_field_00017.dat.
Writing solution file op_00017.dat.
Iteration: 180 Time: 4.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5825E-02 Conservation loss: 1.0799E-16
Writing solution file advection_field_00018.dat.
Writing solution file op_00018.dat.
Iteration: 190 Time: 4.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5820E-02 Conservation loss: 7.5894E-17
Writing solution file advection_field_00019.dat.
Writing solution file op_00019.dat.
Iteration: 200 Time: 5.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5813E-02 Conservation loss: 7.3292E-17
Writing solution file advection_field_00020.dat.
Writing solution file op_00020.dat.
Iteration: 210 Time: 5.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5805E-02 Conservation loss: 4.5536E-17
Writing solution file advection_field_00021.dat.
Writing solution file op_00021.dat.
Iteration: 220 Time: 5.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5798E-02 Conservation loss: 5.5945E-17
Writing solution file advection_field_00022.dat.
Writing solution file op_00022.dat.
Iteration: 230 Time: 5.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5793E-02 Conservation loss: 1.0105E-16
Writing solution file advection_field_00023.dat.
Writing solution file op_00023.dat.
Iteration: 240 Time: 6.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5790E-02 Conservation loss: 8.3700E-17
Writing solution file advection_field_00024.dat.
Writing solution file op_00024.dat.
Iteration: 250 Time: 6.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5790E-02 Conservation loss: 1.6914E-17
Writing solution file advection_field_00025.dat.
Writing solution file op_00025.dat.
Iteration: 260 Time: 6.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5792E-02 Conservation loss: 1.0365E-16
Writing solution file advection_field_00026.dat.
Writing solution file op_00026.dat.
Iteration: 270 Time: 6.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5798E-02 Conservation loss: 8.8037E-17
Writing solution file advection_field_00027.dat.
Writing solution file op_00027.dat.
Iteration: 280 Time: 7.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5804E-02 Conservation loss: 4.7705E-18
Writing solution file advection_field_00028.dat.
Writing solution file op_00028.dat.
Iteration: 290 Time: 7.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5812E-02 Conservation loss: 3.9465E-17
Writing solution file advection_field_00029.dat.
Writing solution file op_00029.dat.
Iteration: 300 Time: 7.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5819E-02 Conservation loss: 4.3368E-19
Writing solution file advection_field_00030.dat.
Writing solution file op_00030.dat.
Iteration: 310 Time: 7.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5825E-02 Conservation loss: 6.2884E-17
Writing solution file advection_field_00031.dat.
Writing solution file op_00031.dat.
Iteration: 320 Time: 8.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5828E-02 Conservation loss: 7.1015E-17
Writing solution file advection_field_00032.dat.
Writing solution file op_00032.dat.
Iteration: 330 Time: 8.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5828E-02 Conservation loss: 1.0473E-16
Writing solution file advection_field_00033.dat.
Writing solution file op_00033.dat.
Iteration: 340 Time: 8.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5826E-02 Conservation loss: 3.4261E-17
Writing solution file advection_field_00034.dat.
Writing solution file op_00034.dat.
Iteration: 350 Time: 8.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5821E-02 Conservation loss: 7.5894E-17
Writing solution file advection_field_00035.dat.
Writing solution file op_00035.dat.
Iteration: 360 Time: 9.000E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5815E-02 Conservation loss: 1.9516E-17
Writing solution file advection_field_00036.dat.
Writing solution file op_00036.dat.
Iteration: 370 Time: 9.250E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5807E-02 Conservation loss: 8.3700E-17
Writing solution file advection_field_00037.dat.
Writing solution file op_00037.dat.
Iteration: 380 Time: 9.500E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5800E-02 Conservation loss: 1.0105E-16
Writing solution file advection_field_00038.dat.
Writing solution file op_00038.dat.
Iteration: 390 Time: 9.750E-01 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5794E-02 Conservation loss: 7.3292E-17
Writing solution file advection_field_00039.dat.
Writing solution file op_00039.dat.
Iteration: 400 Time: 1.000E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5790E-02 Conservation loss: 7.3726E-18
Writing solution file advection_field_00040.dat.
Writing solution file op_00040.dat.
Iteration: 410 Time: 1.025E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5788E-02 Conservation loss: 5.5945E-17
Writing solution file advection_field_00041.dat.
Writing solution file op_00041.dat.
Iteration: 420 Time: 1.050E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5790E-02 Conservation loss: 5.2475E-17
Writing solution file advection_field_00042.dat.
Writing solution file op_00042.dat.
Iteration: 430 Time: 1.075E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5795E-02 Conservation loss: 5.0741E-17
Writing solution file advection_field_00043.dat.
Writing solution file op_00043.dat.
Iteration: 440 Time: 1.100E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5801E-02 Conservation loss: 2.2118E-17
Writing solution file advection_field_00044.dat.
Writing solution file op_00044.dat.
Iteration: 450 Time: 1.125E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5809E-02 Conservation loss: 3.7730E-17
Writing solution file advection_field_00045.dat.
Writing solution file op_00045.dat.
Iteration: 460 Time: 1.150E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5816E-02 Conservation loss: 1.1146E-16
Writing solution file advection_field_00046.dat.
Writing solution file op_00046.dat.
Iteration: 470 Time: 1.175E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5822E-02 Conservation loss: 2.8666E-16
Writing solution file advection_field_00047.dat.
Writing solution file op_00047.dat.
Iteration: 480 Time: 1.200E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 1.3379E-16
Writing solution file advection_field_00048.dat.
Writing solution file op_00048.dat.
Iteration: 490 Time: 1.225E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5828E-02 Conservation loss: 1.4246E-16
Writing solution file advection_field_00049.dat.
Writing solution file op_00049.dat.
Iteration: 500 Time: 1.250E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 1.1623E-16
Writing solution file advection_field_00050.dat.
Writing solution file op_00050.dat.
Iteration: 510 Time: 1.275E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5822E-02 Conservation loss: 1.8258E-16
Writing solution file advection_field_00051.dat.
Writing solution file op_00051.dat.
Iteration: 520 Time: 1.300E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5816E-02 Conservation loss: 2.0383E-17
Writing solution file advection_field_00052.dat.
Writing solution file op_00052.dat.
Iteration: 530 Time: 1.325E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5809E-02 Conservation loss: 4.3802E-17
Writing solution file advection_field_00053.dat.
Writing solution file op_00053.dat.
Iteration: 540 Time: 1.350E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5801E-02 Conservation loss: 9.9313E-17
Writing solution file advection_field_00054.dat.
Writing solution file op_00054.dat.
Iteration: 550 Time: 1.375E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5794E-02 Conservation loss: 7.3292E-17
Writing solution file advection_field_00055.dat.
Writing solution file op_00055.dat.
Iteration: 560 Time: 1.400E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5789E-02 Conservation loss: 2.8189E-17
Writing solution file advection_field_00056.dat.
Writing solution file op_00056.dat.
Iteration: 570 Time: 1.425E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5787E-02 Conservation loss: 1.7781E-17
Writing solution file advection_field_00057.dat.
Writing solution file op_00057.dat.
Iteration: 580 Time: 1.450E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5788E-02 Conservation loss: 7.3726E-18
Writing solution file advection_field_00058.dat.
Writing solution file op_00058.dat.
Iteration: 590 Time: 1.475E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5792E-02 Conservation loss: 7.8496E-17
Writing solution file advection_field_00059.dat.
Writing solution file op_00059.dat.
Iteration: 600 Time: 1.500E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5798E-02 Conservation loss: 1.0278E-16
Writing solution file advection_field_00060.dat.
Writing solution file op_00060.dat.
Iteration: 610 Time: 1.525E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5805E-02 Conservation loss: 1.2880E-16
Writing solution file advection_field_00061.dat.
Writing solution file op_00061.dat.
Iteration: 620 Time: 1.550E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5813E-02 Conservation loss: 5.4210E-17
Writing solution file advection_field_00062.dat.
Writing solution file op_00062.dat.
Iteration: 630 Time: 1.575E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5820E-02 Conservation loss: 1.7217E-16
Writing solution file advection_field_00063.dat.
Writing solution file op_00063.dat.
Iteration: 640 Time: 1.600E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5825E-02 Conservation loss: 3.9682E-17
Writing solution file advection_field_00064.dat.
Writing solution file op_00064.dat.
Iteration: 650 Time: 1.625E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 1.1520E-16
Writing solution file advection_field_00065.dat.
Writing solution file op_00065.dat.
Iteration: 660 Time: 1.650E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 1.3444E-17
Writing solution file advection_field_00066.dat.
Writing solution file op_00066.dat.
Iteration: 670 Time: 1.675E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5824E-02 Conservation loss: 2.3202E-16
Writing solution file advection_field_00067.dat.
Writing solution file op_00067.dat.
Iteration: 680 Time: 1.700E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5818E-02 Conservation loss: 1.2880E-16
Writing solution file advection_field_00068.dat.
Writing solution file op_00068.dat.
Iteration: 690 Time: 1.725E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5810E-02 Conservation loss: 2.2595E-16
Writing solution file advection_field_00069.dat.
Writing solution file op_00069.dat.
Iteration: 700 Time: 1.750E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5802E-02 Conservation loss: 2.1554E-16
Writing solution file advection_field_00070.dat.
Writing solution file op_00070.dat.
Iteration: 710 Time: 1.775E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5795E-02 Conservation loss: 1.4268E-16
Writing solution file advection_field_00071.dat.
Writing solution file op_00071.dat.
Iteration: 720 Time: 1.800E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5790E-02 Conservation loss: 2.2595E-16
Writing solution file advection_field_00072.dat.
Writing solution file op_00072.dat.
Iteration: 730 Time: 1.825E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5786E-02 Conservation loss: 2.0166E-16
Writing solution file advection_field_00073.dat.
Writing solution file op_00073.dat.
Iteration: 740 Time: 1.850E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5786E-02 Conservation loss: 1.7391E-16
Writing solution file advection_field_00074.dat.
Writing solution file op_00074.dat.
Iteration: 750 Time: 1.875E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5789E-02 Conservation loss: 1.7564E-16
Writing solution file advection_field_00075.dat.
Writing solution file op_00075.dat.
Iteration: 760 Time: 1.900E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5795E-02 Conservation loss: 7.5027E-17
Writing solution file advection_field_00076.dat.
Writing solution file op_00076.dat.
Iteration: 770 Time: 1.925E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5802E-02 Conservation loss: 2.6064E-16
Writing solution file advection_field_00077.dat.
Writing solution file op_00077.dat.
Iteration: 780 Time: 1.950E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5810E-02 Conservation loss: 9.2374E-17
Writing solution file advection_field_00078.dat.
Writing solution file op_00078.dat.
Iteration: 790 Time: 1.975E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5817E-02 Conservation loss: 3.0748E-16
Writing solution file advection_field_00079.dat.
Writing solution file op_00079.dat.
Iteration: 800 Time: 2.000E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5823E-02 Conservation loss: 2.3028E-16
Writing solution file advection_field_00080.dat.
Writing solution file op_00080.dat.
Iteration: 810 Time: 2.025E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5826E-02 Conservation loss: 3.2737E-16
Writing solution file advection_field_00081.dat.
Writing solution file op_00081.dat.
Iteration: 820 Time: 2.050E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 1.3921E-16
Writing solution file advection_field_00082.dat.
Writing solution file op_00082.dat.
Iteration: 830 Time: 2.075E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5824E-02 Conservation loss: 1.4311E-16
Writing solution file advection_field_00083.dat.
Writing solution file op_00083.dat.
Iteration: 840 Time: 2.100E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5819E-02 Conservation loss: 2.7972E-16
Writing solution file advection_field_00084.dat.
Writing solution file op_00084.dat.
Iteration: 850 Time: 2.125E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5812E-02 Conservation loss: 2.1207E-16
Writing solution file advection_field_00085.dat.
Writing solution file op_00085.dat.
Iteration: 860 Time: 2.150E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5804E-02 Conservation loss: 1.3227E-16
Writing solution file advection_field_00086.dat.
Writing solution file op_00086.dat.
Iteration: 870 Time: 2.175E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5796E-02 Conservation loss: 1.4789E-16
Writing solution file advection_field_00087.dat.
Writing solution file op_00087.dat.
Iteration: 880 Time: 2.200E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5790E-02 Conservation loss: 1.4962E-16
Writing solution file advection_field_00088.dat.
Writing solution file op_00088.dat.
Iteration: 890 Time: 2.225E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5786E-02 Conservation loss: 2.3636E-16
Writing solution file advection_field_00089.dat.
Writing solution file op_00089.dat.
Iteration: 900 Time: 2.250E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5785E-02 Conservation loss: 1.2186E-16
Writing solution file advection_field_00090.dat.
Writing solution file op_00090.dat.
Iteration: 910 Time: 2.275E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5787E-02 Conservation loss: 2.3289E-16
Writing solution file advection_field_00091.dat.
Writing solution file op_00091.dat.
Iteration: 920 Time: 2.300E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5792E-02 Conservation loss: 2.2595E-16
Writing solution file advection_field_00092.dat.
Writing solution file op_00092.dat.
Iteration: 930 Time: 2.325E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5798E-02 Conservation loss: 1.8258E-16
Writing solution file advection_field_00093.dat.
Writing solution file op_00093.dat.
Iteration: 940 Time: 2.350E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5806E-02 Conservation loss: 2.1554E-16
Writing solution file advection_field_00094.dat.
Writing solution file op_00094.dat.
Iteration: 950 Time: 2.375E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5814E-02 Conservation loss: 1.4875E-16
Writing solution file advection_field_00095.dat.
Writing solution file op_00095.dat.
Iteration: 960 Time: 2.400E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5821E-02 Conservation loss: 3.1398E-16
Writing solution file advection_field_00096.dat.
Writing solution file op_00096.dat.
Iteration: 970 Time: 2.425E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5825E-02 Conservation loss: 2.6064E-16
Writing solution file advection_field_00097.dat.
Writing solution file op_00097.dat.
Iteration: 980 Time: 2.450E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5827E-02 Conservation loss: 2.1576E-16
Writing solution file advection_field_00098.dat.
Writing solution file op_00098.dat.
Iteration: 990 Time: 2.475E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5825E-02 Conservation loss: 2.1250E-16
Writing solution file advection_field_00099.dat.
Writing solution file op_00099.dat.
Iteration: 1000 Time: 2.500E+00 Max CFL: 3.000E-01 Max Diff. No.: 0.000E+00 Norm: 1.5820E-02 Conservation loss: 1.5049E-16
Writing solution file advection_field_00100.dat.
Writing solution file op_00100.dat.
Completed time integration (Final time: 2.500000).
Computed errors for domain 0:
L1 Error : 0.0000000000000000E+00
L2 Error : 0.0000000000000000E+00
Linfinity Error : 0.0000000000000000E+00
Conservation Errors:
1.5048726154098802E-16
Solver runtime (in seconds): 1.4122250000000001E+00
Total runtime (in seconds): 1.4212039999999999E+00
Deallocating arrays.
Finished.