2D Shallow Water Equations - Latitude Belt Flow
Location: hypar/Examples/2D/ShallowWater2D/LatitudeBeltFlow (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: 2D Shallow Water Equations (shallowwater2d.h)
References:
- Zhu, Et. al., "Variational Data Assimilation with a Variable Resolution
Finite-Element Shallow-Water Equations Model", Monthly Weather Review, 122, 1994, pp. 946–965.
Govering equations and approximation of Coriolis forces: Eqns (2.1)-(2.4)
Problem definition: Eqns. (4.1)-(4.3)
Domain: \(0 \le x \le 6,000,000\,{\rm m}, 0\le y \le 4,400,000\,{\rm m}\), "periodic" (_PERIODIC_) boundaries along x, "slip wall" (_SW_SLIP_WALL_) boundaries along y.
Initial solution: See equations (4.1) and (4.2) in reference, constant (zero) bottom topography
Other parameters:
- \(g=10\) (ShallowWater2D::g)
- \(\hat{f}=0.0001\) (ShallowWater2D::fhat)
- \(\beta = 1.5\times 10^{-11}\) (ShallowWater2D::beta)
- \(D=4400000\) (ShallowWater2D::D)
Numerical Method:
- Spatial discretization (hyperbolic): 5th order WENO (Interp1PrimFifthOrderWENO())
- Time integration: RK4 (TimeRK(), _RK_44_)
Input files required:
Note: in addition to the usual input files that HyPar needs, this physical model needs the following input file(s):
- topography.inp : file containing the bottom topography (same format as initial.inp).
However, this case has a constant (zero) bottom topography, and thus this file can be skipped.
solver.inp
begin
ndims 2
nvars 3
size 150 120
iproc 2 2
ghost 3
n_iter 2000
restart_iter 0
time_scheme rk
time_scheme_type 44
hyp_space_scheme weno5
hyp_interp_type components
dt 180
conservation_check yes
screen_op_iter 20
file_op_iter 20
op_file_format text
ip_file_type ascii
input_mode serial
output_mode serial
op_overwrite no
model shallow-water-2d
end
boundary.inp
4
periodic 0 1 0 0 0 4400000.0
periodic 0 -1 0 0 0 4400000.0
shallow-water-slip-wall 1 1 0 6000000.0 0 0
0.0 0.0
shallow-water-slip-wall 1 -1 0 6000000.0 0 0
0.0 0.0
physics.inp
begin
gravity 10.0
topography_type 0
coriolis_fhat 0.0001
coriolis_beta 1.5e-11
coriolis_D 4400000
upwinding llf-char
end
weno.inp (optional)
begin
mapped 0
borges 0
yc 1
no_limiting 0
epsilon 1.0e-6
p 2
rc 0.3
xi 0.001
tol 1e-16
end
To generate initial.inp and topography.inp, compile and run the following code in the run directory (note: topography.inp can be skipped since this case involves a uniform topography).
/*
Code to generate the initial solution for:
Case: Limited Area Channel Flow
Model: ShallowWater2D
References:
Zhu, Et. al., "Variational Data Assimilation with a Variable Resolution
Finite-Element Shallow-Water Equations Model", Monthly Weather Review,
122, 1994, pp. 946--965
http://dx.doi.org/10.1175/1520-0493(1994)122%3C0946:VDAWAV%3E2.0.CO;2
Eqns. (4.1)-(4.3)
Needs: solver.inp
Writes out: initial.inp
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
/* some global parameters */
double L = 6000000.0,
D = 4400000.0,
g = 10.0,
fhat = 1e-4,
beta = 1.5e-11,
H0 = 2000.0,
H1 = 220.0,
H2 = 133.0;
double hfunction(double x,double y) {
double pi = 4.0*atan(1.0);
double h = H0 + H1*tanh((9.0*(0.5*D-y))/(2.0*D))
+ H2 * (1.0/cosh(9.0*(0.5*D-y)/D)) * (1.0/cosh(9.0*(0.5*D-y)/D)) * sin(2*pi*x/L);
return(h);
}
int main(){
int NI = 15, NJ = 12, ndims = 2;
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);
fscanf(in,"%d",&NJ);
} 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 != 2) {
printf("ndims is not 2 in solver.inp. this code is to generate 2D initial conditions\n");
return(0);
}
printf("Grid:\t\t\t%d X %d\n",NI,NJ);
int i,j;
double dx = L / ((double)NI);
double dy = D / ((double)NJ-1);
double *x, *y, *u0, *u1, *u2;
x = (double*) calloc (NI , sizeof(double));
y = (double*) calloc (NJ , sizeof(double));
u0 = (double*) calloc (NI*NJ, sizeof(double));
u1 = (double*) calloc (NI*NJ, sizeof(double));
u2 = (double*) calloc (NI*NJ, sizeof(double));
for (i = 0; i < NI; i++){
for (j = 0; j < NJ; j++){
x[i] = i*dx;
y[j] = j*dy;
int p = NI*j + i;
double h, u, v, hE, hW, hN, hS;
h = hfunction(x[i],y[j]);
hE = hfunction(x[i]+dx,y[j]);
hW = hfunction(x[i]-dx,y[j]);
hN = hfunction(x[i],y[j]+dy);
hS = hfunction(x[i],y[j]-dy);
double f = fhat + beta * (y[j] - 0.5*D);
double h_x, h_y;
h_x = (hE - hW) / (2*dx);
h_y = (hN - hS) / (2*dy);
u = -(g/f) * h_y;
v = (g/f) * h_x;
u0[p] = h;
u1[p] = h*u;
u2[p] = h*v;
}
}
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 (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = NI*j + i;
fprintf(out,"%1.16e ",u0[p]);
}
}
fprintf(out,"\n");
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = NI*j + i;
fprintf(out,"%1.16e ",u1[p]);
}
}
fprintf(out,"\n");
for (j = 0; j < NJ; j++) {
for (i = 0; i < NI; i++) {
int p = NI*j + i;
fprintf(out,"%1.16e ",u2[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);
double *U = (double*) calloc (3*NI*NJ,sizeof(double));
for (i=0; i < NI; i++) {
for (j = 0; j < NJ; j++) {
int p = NI*j + i;
U[3*p+0] = u0[p];
U[3*p+1] = u1[p];
U[3*p+2] = u2[p];
}
}
fwrite(U,sizeof(double),3*NI*NJ,out);
free(U);
fclose(out);
}
free(x);
free(y);
free(u0);
free(u1);
free(u2);
return(0);
}
Output:
Note that iproc is set to
2 2
in solver.inp (i.e., 2 processors along x, and 2 processors along y). Thus, this example should be run with 4 MPI ranks (or change iproc).
After running the code, there should be 101 solution output files op_00000.dat, ..., op_00100.dat; the first one is the solution at \(t=0\) and the final one is the solution at \(t=360000\). 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 text in solver.inp, and thus, all the files are in plain text (ASCII) format. In these files, the data is written out as: the first two columns are grid indices, the next two columns are the x and y coordinates, and the remaining columns are the three solution components. HyPar::op_file_format can also be set to tecplot2d to get the solution files in the Tecplot format (that can be read using any visualization software that supports Tecplot format).
The following plot shows an animation of the solution:
It was obtained by using the following MATLAB code:
clear all;
close all;
fname_indices = input('Enter range of file indices to plot: ');
% Load initial solution file
data = load('op_00000.dat');
% find out max grid sizes
imax = max(data(:,1)) + 1;
jmax = max(data(:,2)) + 1;
%spatial coordinates
x = reshape(data(:,3),imax,jmax);
y = reshape(data(:,4),imax,jmax);
count = 0;
for i = fname_indices
fname = strcat('op_',sprintf('%05d',i),'.dat');
% read solution
data = load(fname);
h = reshape(data(:,5),imax,jmax);
u = reshape(data(:,6),imax,jmax)./h;
v = reshape(data(:,7),imax,jmax)./h;
% plot
scrsz = get(0,'screensize');
width = 0.9*scrsz(3);
figure(1);
set(1,'Position',[0 0 width 0.8*width]);
surf(x,y,h);
view(100,60);
colorbar;
filename = ['fig_',sprintf('%05d',count),'.png'];
print(1,filename,'-dpng');
count = count+1;
end
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:
150 120 2 2 1.8000000000000000E+02 3.0050505050505077E-16 5.4521365427062857E-04 1.5985329391656518E+15
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 of each component(HyPar::ConservationError). Note that that conservation error for the water height is zero to machine precision (the non-zero conservation "error" for the momentum components is due to the non-zero source term - Coriolis force).
Expected screen output:
HyPar - Parallel (MPI) version with 4 processes
Compiled with PETSc time integration.
Reading solver inputs from file "solver.inp".
No. of dimensions : 2
No. of variables : 3
Domain size : 150 120
Processes along each dimension : 2 2
No. of ghosts pts : 3
No. of iter. : 2000
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-1stage
Spatial discretization scheme (parabolic ) : 2
Time Step : 1.800000E+02
Check for conservation : yes
Screen output iterations : 20
File output iterations : 20
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 : shallow-water-2d
Partitioning domain.
Allocating data arrays.
Reading array from ASCII file initial.inp (Serial mode).
Volume integral of the initial solution:
0: 5.3243697478991552E+16
1: 5.2823596148641619E+17
2: -5.9375000000000000E+00
Reading boundary conditions from "boundary.inp".
Boundary periodic: Along dimension 0 and face +1
Boundary periodic: Along dimension 0 and face -1
Boundary shallow-water-slip-wall: Along dimension 1 and face +1
Boundary shallow-water-slip-wall: Along dimension 1 and face -1
4 boundary condition(s) read.
Initializing solvers.
Reading WENO parameters from weno.inp.
Initializing physics. Model = "shallow-water-2d"
Reading physical model inputs from file "physics.inp".
Setting up time integration.
Solving in time (from 0 to 2000 iterations)
Writing solution file op_00000.dat.
Iteration: 20 Time: 3.600E+03 Max CFL: 8.283E-01 Max Diff. No.: -1.000E+00 Norm: 4.4377E+02 Conservation loss: 1.5678E+13
Writing solution file op_00001.dat.
Iteration: 40 Time: 7.200E+03 Max CFL: 8.317E-01 Max Diff. No.: -1.000E+00 Norm: 3.9860E+02 Conservation loss: 3.1416E+13
Writing solution file op_00002.dat.
Iteration: 60 Time: 1.080E+04 Max CFL: 8.309E-01 Max Diff. No.: -1.000E+00 Norm: 3.3905E+02 Conservation loss: 4.7255E+13
Writing solution file op_00003.dat.
Iteration: 80 Time: 1.440E+04 Max CFL: 8.313E-01 Max Diff. No.: -1.000E+00 Norm: 3.0518E+02 Conservation loss: 6.3217E+13
Writing solution file op_00004.dat.
Iteration: 100 Time: 1.800E+04 Max CFL: 8.289E-01 Max Diff. No.: -1.000E+00 Norm: 2.4485E+02 Conservation loss: 7.9308E+13
Writing solution file op_00005.dat.
Iteration: 120 Time: 2.160E+04 Max CFL: 8.247E-01 Max Diff. No.: -1.000E+00 Norm: 3.8857E+02 Conservation loss: 9.5503E+13
Writing solution file op_00006.dat.
Iteration: 140 Time: 2.520E+04 Max CFL: 8.258E-01 Max Diff. No.: -1.000E+00 Norm: 4.4309E+02 Conservation loss: 1.1174E+14
Writing solution file op_00007.dat.
Iteration: 160 Time: 2.880E+04 Max CFL: 8.270E-01 Max Diff. No.: -1.000E+00 Norm: 4.9726E+02 Conservation loss: 1.2797E+14
Writing solution file op_00008.dat.
Iteration: 180 Time: 3.240E+04 Max CFL: 8.291E-01 Max Diff. No.: -1.000E+00 Norm: 5.0514E+02 Conservation loss: 1.4414E+14
Writing solution file op_00009.dat.
Iteration: 200 Time: 3.600E+04 Max CFL: 8.401E-01 Max Diff. No.: -1.000E+00 Norm: 5.2483E+02 Conservation loss: 1.6016E+14
Writing solution file op_00010.dat.
Iteration: 220 Time: 3.960E+04 Max CFL: 8.306E-01 Max Diff. No.: -1.000E+00 Norm: 4.9425E+02 Conservation loss: 1.7616E+14
Writing solution file op_00011.dat.
Iteration: 240 Time: 4.320E+04 Max CFL: 8.215E-01 Max Diff. No.: -1.000E+00 Norm: 4.6916E+02 Conservation loss: 1.9223E+14
Writing solution file op_00012.dat.
Iteration: 260 Time: 4.680E+04 Max CFL: 8.213E-01 Max Diff. No.: -1.000E+00 Norm: 3.7173E+02 Conservation loss: 2.0834E+14
Writing solution file op_00013.dat.
Iteration: 280 Time: 5.040E+04 Max CFL: 8.184E-01 Max Diff. No.: -1.000E+00 Norm: 5.0904E+02 Conservation loss: 2.2445E+14
Writing solution file op_00014.dat.
Iteration: 300 Time: 5.400E+04 Max CFL: 8.127E-01 Max Diff. No.: -1.000E+00 Norm: 5.4971E+02 Conservation loss: 2.4052E+14
Writing solution file op_00015.dat.
Iteration: 320 Time: 5.760E+04 Max CFL: 8.025E-01 Max Diff. No.: -1.000E+00 Norm: 6.0587E+02 Conservation loss: 2.5651E+14
Writing solution file op_00016.dat.
Iteration: 340 Time: 6.120E+04 Max CFL: 8.302E-01 Max Diff. No.: -1.000E+00 Norm: 6.5132E+02 Conservation loss: 2.7238E+14
Writing solution file op_00017.dat.
Iteration: 360 Time: 6.480E+04 Max CFL: 8.288E-01 Max Diff. No.: -1.000E+00 Norm: 6.9250E+02 Conservation loss: 2.8810E+14
Writing solution file op_00018.dat.
Iteration: 380 Time: 6.840E+04 Max CFL: 8.277E-01 Max Diff. No.: -1.000E+00 Norm: 6.7591E+02 Conservation loss: 3.0377E+14
Writing solution file op_00019.dat.
Iteration: 400 Time: 7.200E+04 Max CFL: 8.465E-01 Max Diff. No.: -1.000E+00 Norm: 6.5968E+02 Conservation loss: 3.1944E+14
Writing solution file op_00020.dat.
Iteration: 420 Time: 7.560E+04 Max CFL: 8.571E-01 Max Diff. No.: -1.000E+00 Norm: 6.3826E+02 Conservation loss: 3.3523E+14
Writing solution file op_00021.dat.
Iteration: 440 Time: 7.920E+04 Max CFL: 8.574E-01 Max Diff. No.: -1.000E+00 Norm: 6.2022E+02 Conservation loss: 3.5126E+14
Writing solution file op_00022.dat.
Iteration: 460 Time: 8.280E+04 Max CFL: 8.574E-01 Max Diff. No.: -1.000E+00 Norm: 6.7470E+02 Conservation loss: 3.6753E+14
Writing solution file op_00023.dat.
Iteration: 480 Time: 8.640E+04 Max CFL: 8.560E-01 Max Diff. No.: -1.000E+00 Norm: 7.0703E+02 Conservation loss: 3.8395E+14
Writing solution file op_00024.dat.
Iteration: 500 Time: 9.000E+04 Max CFL: 8.465E-01 Max Diff. No.: -1.000E+00 Norm: 7.3248E+02 Conservation loss: 4.0034E+14
Writing solution file op_00025.dat.
Iteration: 520 Time: 9.360E+04 Max CFL: 8.318E-01 Max Diff. No.: -1.000E+00 Norm: 7.6668E+02 Conservation loss: 4.1655E+14
Writing solution file op_00026.dat.
Iteration: 540 Time: 9.720E+04 Max CFL: 8.480E-01 Max Diff. No.: -1.000E+00 Norm: 7.9167E+02 Conservation loss: 4.3260E+14
Writing solution file op_00027.dat.
Iteration: 560 Time: 1.008E+05 Max CFL: 8.412E-01 Max Diff. No.: -1.000E+00 Norm: 7.8038E+02 Conservation loss: 4.4859E+14
Writing solution file op_00028.dat.
Iteration: 580 Time: 1.044E+05 Max CFL: 8.438E-01 Max Diff. No.: -1.000E+00 Norm: 7.5727E+02 Conservation loss: 4.6459E+14
Writing solution file op_00029.dat.
Iteration: 600 Time: 1.080E+05 Max CFL: 8.545E-01 Max Diff. No.: -1.000E+00 Norm: 7.2991E+02 Conservation loss: 4.8061E+14
Writing solution file op_00030.dat.
Iteration: 620 Time: 1.116E+05 Max CFL: 8.559E-01 Max Diff. No.: -1.000E+00 Norm: 8.1845E+02 Conservation loss: 4.9669E+14
Writing solution file op_00031.dat.
Iteration: 640 Time: 1.152E+05 Max CFL: 8.547E-01 Max Diff. No.: -1.000E+00 Norm: 8.9818E+02 Conservation loss: 5.1283E+14
Writing solution file op_00032.dat.
Iteration: 660 Time: 1.188E+05 Max CFL: 8.472E-01 Max Diff. No.: -1.000E+00 Norm: 9.2536E+02 Conservation loss: 5.2900E+14
Writing solution file op_00033.dat.
Iteration: 680 Time: 1.224E+05 Max CFL: 8.337E-01 Max Diff. No.: -1.000E+00 Norm: 9.3209E+02 Conservation loss: 5.4510E+14
Writing solution file op_00034.dat.
Iteration: 700 Time: 1.260E+05 Max CFL: 8.180E-01 Max Diff. No.: -1.000E+00 Norm: 9.3946E+02 Conservation loss: 5.6103E+14
Writing solution file op_00035.dat.
Iteration: 720 Time: 1.296E+05 Max CFL: 8.961E-01 Max Diff. No.: -1.000E+00 Norm: 9.5910E+02 Conservation loss: 5.7679E+14
Writing solution file op_00036.dat.
Iteration: 740 Time: 1.332E+05 Max CFL: 9.198E-01 Max Diff. No.: -1.000E+00 Norm: 9.1544E+02 Conservation loss: 5.9244E+14
Writing solution file op_00037.dat.
Iteration: 760 Time: 1.368E+05 Max CFL: 9.233E-01 Max Diff. No.: -1.000E+00 Norm: 9.2664E+02 Conservation loss: 6.0814E+14
Writing solution file op_00038.dat.
Iteration: 780 Time: 1.404E+05 Max CFL: 9.109E-01 Max Diff. No.: -1.000E+00 Norm: 8.1109E+02 Conservation loss: 6.2407E+14
Writing solution file op_00039.dat.
Iteration: 800 Time: 1.440E+05 Max CFL: 9.114E-01 Max Diff. No.: -1.000E+00 Norm: 8.7863E+02 Conservation loss: 6.4024E+14
Writing solution file op_00040.dat.
Iteration: 820 Time: 1.476E+05 Max CFL: 9.080E-01 Max Diff. No.: -1.000E+00 Norm: 9.1852E+02 Conservation loss: 6.5657E+14
Writing solution file op_00041.dat.
Iteration: 840 Time: 1.512E+05 Max CFL: 8.830E-01 Max Diff. No.: -1.000E+00 Norm: 9.3299E+02 Conservation loss: 6.7294E+14
Writing solution file op_00042.dat.
Iteration: 860 Time: 1.548E+05 Max CFL: 8.670E-01 Max Diff. No.: -1.000E+00 Norm: 9.7294E+02 Conservation loss: 6.8921E+14
Writing solution file op_00043.dat.
Iteration: 880 Time: 1.584E+05 Max CFL: 8.543E-01 Max Diff. No.: -1.000E+00 Norm: 1.0055E+03 Conservation loss: 7.0535E+14
Writing solution file op_00044.dat.
Iteration: 900 Time: 1.620E+05 Max CFL: 9.014E-01 Max Diff. No.: -1.000E+00 Norm: 9.9412E+02 Conservation loss: 7.2134E+14
Writing solution file op_00045.dat.
Iteration: 920 Time: 1.656E+05 Max CFL: 9.026E-01 Max Diff. No.: -1.000E+00 Norm: 9.9431E+02 Conservation loss: 7.3723E+14
Writing solution file op_00046.dat.
Iteration: 940 Time: 1.692E+05 Max CFL: 8.907E-01 Max Diff. No.: -1.000E+00 Norm: 9.8222E+02 Conservation loss: 7.5317E+14
Writing solution file op_00047.dat.
Iteration: 960 Time: 1.728E+05 Max CFL: 8.859E-01 Max Diff. No.: -1.000E+00 Norm: 8.9608E+02 Conservation loss: 7.6921E+14
Writing solution file op_00048.dat.
Iteration: 980 Time: 1.764E+05 Max CFL: 8.831E-01 Max Diff. No.: -1.000E+00 Norm: 9.9049E+02 Conservation loss: 7.8532E+14
Writing solution file op_00049.dat.
Iteration: 1000 Time: 1.800E+05 Max CFL: 8.782E-01 Max Diff. No.: -1.000E+00 Norm: 1.0100E+03 Conservation loss: 8.0144E+14
Writing solution file op_00050.dat.
Iteration: 1020 Time: 1.836E+05 Max CFL: 8.531E-01 Max Diff. No.: -1.000E+00 Norm: 1.0175E+03 Conservation loss: 8.1747E+14
Writing solution file op_00051.dat.
Iteration: 1040 Time: 1.872E+05 Max CFL: 8.405E-01 Max Diff. No.: -1.000E+00 Norm: 1.0173E+03 Conservation loss: 8.3339E+14
Writing solution file op_00052.dat.
Iteration: 1060 Time: 1.908E+05 Max CFL: 8.370E-01 Max Diff. No.: -1.000E+00 Norm: 1.0216E+03 Conservation loss: 8.4918E+14
Writing solution file op_00053.dat.
Iteration: 1080 Time: 1.944E+05 Max CFL: 8.579E-01 Max Diff. No.: -1.000E+00 Norm: 9.9908E+02 Conservation loss: 8.6485E+14
Writing solution file op_00054.dat.
Iteration: 1100 Time: 1.980E+05 Max CFL: 8.750E-01 Max Diff. No.: -1.000E+00 Norm: 9.6644E+02 Conservation loss: 8.8047E+14
Writing solution file op_00055.dat.
Iteration: 1120 Time: 2.016E+05 Max CFL: 8.804E-01 Max Diff. No.: -1.000E+00 Norm: 9.6455E+02 Conservation loss: 8.9625E+14
Writing solution file op_00056.dat.
Iteration: 1140 Time: 2.052E+05 Max CFL: 8.750E-01 Max Diff. No.: -1.000E+00 Norm: 9.8838E+02 Conservation loss: 9.1226E+14
Writing solution file op_00057.dat.
Iteration: 1160 Time: 2.088E+05 Max CFL: 8.623E-01 Max Diff. No.: -1.000E+00 Norm: 9.4180E+02 Conservation loss: 9.2850E+14
Writing solution file op_00058.dat.
Iteration: 1180 Time: 2.124E+05 Max CFL: 8.385E-01 Max Diff. No.: -1.000E+00 Norm: 9.5401E+02 Conservation loss: 9.4480E+14
Writing solution file op_00059.dat.
Iteration: 1200 Time: 2.160E+05 Max CFL: 8.109E-01 Max Diff. No.: -1.000E+00 Norm: 9.2255E+02 Conservation loss: 9.6099E+14
Writing solution file op_00060.dat.
Iteration: 1220 Time: 2.196E+05 Max CFL: 8.013E-01 Max Diff. No.: -1.000E+00 Norm: 9.4781E+02 Conservation loss: 9.7707E+14
Writing solution file op_00061.dat.
Iteration: 1240 Time: 2.232E+05 Max CFL: 8.562E-01 Max Diff. No.: -1.000E+00 Norm: 9.7646E+02 Conservation loss: 9.9307E+14
Writing solution file op_00062.dat.
Iteration: 1260 Time: 2.268E+05 Max CFL: 8.798E-01 Max Diff. No.: -1.000E+00 Norm: 9.3879E+02 Conservation loss: 1.0090E+15
Writing solution file op_00063.dat.
Iteration: 1280 Time: 2.304E+05 Max CFL: 8.796E-01 Max Diff. No.: -1.000E+00 Norm: 9.0876E+02 Conservation loss: 1.0248E+15
Writing solution file op_00064.dat.
Iteration: 1300 Time: 2.340E+05 Max CFL: 8.863E-01 Max Diff. No.: -1.000E+00 Norm: 8.5053E+02 Conservation loss: 1.0407E+15
Writing solution file op_00065.dat.
Iteration: 1320 Time: 2.376E+05 Max CFL: 8.834E-01 Max Diff. No.: -1.000E+00 Norm: 9.3103E+02 Conservation loss: 1.0567E+15
Writing solution file op_00066.dat.
Iteration: 1340 Time: 2.412E+05 Max CFL: 8.660E-01 Max Diff. No.: -1.000E+00 Norm: 9.3307E+02 Conservation loss: 1.0728E+15
Writing solution file op_00067.dat.
Iteration: 1360 Time: 2.448E+05 Max CFL: 8.314E-01 Max Diff. No.: -1.000E+00 Norm: 9.6442E+02 Conservation loss: 1.0889E+15
Writing solution file op_00068.dat.
Iteration: 1380 Time: 2.484E+05 Max CFL: 8.170E-01 Max Diff. No.: -1.000E+00 Norm: 9.4764E+02 Conservation loss: 1.1048E+15
Writing solution file op_00069.dat.
Iteration: 1400 Time: 2.520E+05 Max CFL: 8.060E-01 Max Diff. No.: -1.000E+00 Norm: 9.6308E+02 Conservation loss: 1.1207E+15
Writing solution file op_00070.dat.
Iteration: 1420 Time: 2.556E+05 Max CFL: 8.301E-01 Max Diff. No.: -1.000E+00 Norm: 9.3390E+02 Conservation loss: 1.1364E+15
Writing solution file op_00071.dat.
Iteration: 1440 Time: 2.592E+05 Max CFL: 8.514E-01 Max Diff. No.: -1.000E+00 Norm: 9.1990E+02 Conservation loss: 1.1520E+15
Writing solution file op_00072.dat.
Iteration: 1460 Time: 2.628E+05 Max CFL: 8.420E-01 Max Diff. No.: -1.000E+00 Norm: 9.0714E+02 Conservation loss: 1.1677E+15
Writing solution file op_00073.dat.
Iteration: 1480 Time: 2.664E+05 Max CFL: 8.506E-01 Max Diff. No.: -1.000E+00 Norm: 8.1822E+02 Conservation loss: 1.1836E+15
Writing solution file op_00074.dat.
Iteration: 1500 Time: 2.700E+05 Max CFL: 8.397E-01 Max Diff. No.: -1.000E+00 Norm: 8.9556E+02 Conservation loss: 1.1997E+15
Writing solution file op_00075.dat.
Iteration: 1520 Time: 2.736E+05 Max CFL: 8.379E-01 Max Diff. No.: -1.000E+00 Norm: 8.9757E+02 Conservation loss: 1.2159E+15
Writing solution file op_00076.dat.
Iteration: 1540 Time: 2.772E+05 Max CFL: 8.407E-01 Max Diff. No.: -1.000E+00 Norm: 8.8750E+02 Conservation loss: 1.2321E+15
Writing solution file op_00077.dat.
Iteration: 1560 Time: 2.808E+05 Max CFL: 8.313E-01 Max Diff. No.: -1.000E+00 Norm: 8.8765E+02 Conservation loss: 1.2483E+15
Writing solution file op_00078.dat.
Iteration: 1580 Time: 2.844E+05 Max CFL: 8.238E-01 Max Diff. No.: -1.000E+00 Norm: 8.9689E+02 Conservation loss: 1.2642E+15
Writing solution file op_00079.dat.
Iteration: 1600 Time: 2.880E+05 Max CFL: 8.199E-01 Max Diff. No.: -1.000E+00 Norm: 9.0169E+02 Conservation loss: 1.2801E+15
Writing solution file op_00080.dat.
Iteration: 1620 Time: 2.916E+05 Max CFL: 8.320E-01 Max Diff. No.: -1.000E+00 Norm: 9.0500E+02 Conservation loss: 1.2960E+15
Writing solution file op_00081.dat.
Iteration: 1640 Time: 2.952E+05 Max CFL: 8.350E-01 Max Diff. No.: -1.000E+00 Norm: 9.0170E+02 Conservation loss: 1.3119E+15
Writing solution file op_00082.dat.
Iteration: 1660 Time: 2.988E+05 Max CFL: 8.239E-01 Max Diff. No.: -1.000E+00 Norm: 9.0937E+02 Conservation loss: 1.3279E+15
Writing solution file op_00083.dat.
Iteration: 1680 Time: 3.024E+05 Max CFL: 8.194E-01 Max Diff. No.: -1.000E+00 Norm: 8.8423E+02 Conservation loss: 1.3439E+15
Writing solution file op_00084.dat.
Iteration: 1700 Time: 3.060E+05 Max CFL: 8.006E-01 Max Diff. No.: -1.000E+00 Norm: 8.7109E+02 Conservation loss: 1.3599E+15
Writing solution file op_00085.dat.
Iteration: 1720 Time: 3.096E+05 Max CFL: 7.987E-01 Max Diff. No.: -1.000E+00 Norm: 8.6286E+02 Conservation loss: 1.3759E+15
Writing solution file op_00086.dat.
Iteration: 1740 Time: 3.132E+05 Max CFL: 7.940E-01 Max Diff. No.: -1.000E+00 Norm: 8.6409E+02 Conservation loss: 1.3918E+15
Writing solution file op_00087.dat.
Iteration: 1760 Time: 3.168E+05 Max CFL: 7.944E-01 Max Diff. No.: -1.000E+00 Norm: 8.6235E+02 Conservation loss: 1.4075E+15
Writing solution file op_00088.dat.
Iteration: 1780 Time: 3.204E+05 Max CFL: 8.094E-01 Max Diff. No.: -1.000E+00 Norm: 8.5935E+02 Conservation loss: 1.4232E+15
Writing solution file op_00089.dat.
Iteration: 1800 Time: 3.240E+05 Max CFL: 8.275E-01 Max Diff. No.: -1.000E+00 Norm: 8.5785E+02 Conservation loss: 1.4389E+15
Writing solution file op_00090.dat.
Iteration: 1820 Time: 3.276E+05 Max CFL: 8.406E-01 Max Diff. No.: -1.000E+00 Norm: 7.7429E+02 Conservation loss: 1.4547E+15
Writing solution file op_00091.dat.
Iteration: 1840 Time: 3.312E+05 Max CFL: 8.289E-01 Max Diff. No.: -1.000E+00 Norm: 8.6605E+02 Conservation loss: 1.4706E+15
Writing solution file op_00092.dat.
Iteration: 1860 Time: 3.348E+05 Max CFL: 8.122E-01 Max Diff. No.: -1.000E+00 Norm: 8.4107E+02 Conservation loss: 1.4868E+15
Writing solution file op_00093.dat.
Iteration: 1880 Time: 3.384E+05 Max CFL: 7.908E-01 Max Diff. No.: -1.000E+00 Norm: 8.2938E+02 Conservation loss: 1.5029E+15
Writing solution file op_00094.dat.
Iteration: 1900 Time: 3.420E+05 Max CFL: 7.941E-01 Max Diff. No.: -1.000E+00 Norm: 8.1713E+02 Conservation loss: 1.5190E+15
Writing solution file op_00095.dat.
Iteration: 1920 Time: 3.456E+05 Max CFL: 7.927E-01 Max Diff. No.: -1.000E+00 Norm: 8.0634E+02 Conservation loss: 1.5350E+15
Writing solution file op_00096.dat.
Iteration: 1940 Time: 3.492E+05 Max CFL: 7.919E-01 Max Diff. No.: -1.000E+00 Norm: 7.9486E+02 Conservation loss: 1.5510E+15
Writing solution file op_00097.dat.
Iteration: 1960 Time: 3.528E+05 Max CFL: 7.989E-01 Max Diff. No.: -1.000E+00 Norm: 7.9769E+02 Conservation loss: 1.5669E+15
Writing solution file op_00098.dat.
Iteration: 1980 Time: 3.564E+05 Max CFL: 8.166E-01 Max Diff. No.: -1.000E+00 Norm: 8.0189E+02 Conservation loss: 1.5827E+15
Writing solution file op_00099.dat.
Iteration: 2000 Time: 3.600E+05 Max CFL: 8.043E-01 Max Diff. No.: -1.000E+00 Norm: 7.2451E+02 Conservation loss: 1.5985E+15
Writing solution file op_00100.dat.
Completed time integration (Final time: 360000.000000).
Computed errors:
L1 Error : 0.0000000000000000E+00
L2 Error : 0.0000000000000000E+00
Linfinity Error : 0.0000000000000000E+00
Conservation Errors:
3.0050505050505077E-16
5.4521365427062857E-04
1.5985329391656518E+15
Solver runtime (in seconds): 3.8254883100000001E+02
Total runtime (in seconds): 3.8260785800000002E+02
Deallocating arrays.
Finished.