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.