1D Linear Advection - Sine Wave
Location: hypar/Examples/1D/LinearAdvection/SineWave_PETSc (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: 1D Linear Advection Equation (linearadr.h)
References:
- Ghosh, D., Baeder, J. D., "Compact Reconstruction Schemes with Weighted ENO Limiting for Hyperbolic Conservation Laws", SIAM Journal on Scientific Computing, 34 (3), 2012, A1678–A1706
Domain: \(0 \le x < 1\), "periodic" (_PERIODIC_) boundary conditions
Initial solution: \(u\left(x,0\right) = \sin\left(2\pi x\right)\)
Numerical Method:
- Spatial discretization (hyperbolic): 5th order CRWENO (Interp1PrimFifthOrderCRWENO())
- Time integration: PETSc (SolvePETSc())
- Method class: Runge-Kutta (TSRK - https://petsc.org/release/docs/manualpages/TS/TSRK.html)
- Specific method: Classical 4th-order RK (TSRK4 - https://petsc.org/release/docs/manualpages/TS/TSRK4.html#TSRK4)
Input files required:
.petscrc
# See PETSc documentation for more details (https://petsc.org/release/overview/).
# Note that if the following are specified in this file, the corresponding inputs in solver.inp are *ignored*.
# + "-ts_dt" (time step size): ignores "dt" in solver.inp
# + "-ts_max_steps" (maximum number of time iterations): ignores "n_iter" in solver.inp
# + "-ts_max_time" (final simulation time): ignores "n_iter" X "dt" in solver.inp
# Use PETSc time-integration
-use-petscts
# Final time
-ts_max_time 1.0
# Time step size
-ts_dt 0.0025
# Maximum number of iterations
-ts_max_steps 400
# Time integration scheme type - explicit RK
-ts_type rk
# RK type - "4" (4th-order, 4-stage)
-ts_rk_type 4
# No time-step adaptivity
-ts_adapt_type none
# Print time step information to screen
-ts_monitor
solver.inp
begin
ndims 1
nvars 1
size 80
iproc 1
ghost 3
n_iter 400
time_scheme rk
time_scheme_type ssprk3
hyp_space_scheme crweno5
conservation_check no
dt 0.0025
screen_op_iter 10
file_op_iter 40
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
begin
advection 1.0
end
lusolver.inp (optional)
begin
reducedsolvetype jacobi
evaluate_norm 1
maxiter 10
atol 1e-12
rtol 1e-10
verbose 0
end
weno.inp (optional)
begin
mapped 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(){
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. 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);
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 != 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;
x = (double*) calloc (NI, sizeof(double));
u = (double*) calloc (NI, sizeof(double));
for (i = 0; i < NI; i++){
x[i] = i*dx;
u[i] = sin(2*pi*x[i]);
}
FILE *out;
if (!strcmp(ip_file_type,"ascii")) {
printf("Writing ASCII initial solution file initial.inp\n");
out = fopen("initial.inp","w");
for (i = 0; i < NI; i++) fprintf(out,"%lf ",x[i]);
fprintf(out,"\n");
for (i = 0; i < NI; i++) fprintf(out,"%lf ",u[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);
}
free(x);
free(u);
return(0);
}
Output:
After running the code, there should be 11 output files op_00000.dat, op_00001.dat, ... op_00010.dat; the first one is the solution at \(t=0\) and the final one is the solution at \(t=1\). 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.
Solutions at t=0,0.5,1: The following figure is obtained by plotting op_00000.dat (initial), op_00005.dat (t=0.5), and op_00010.dat (final).
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:
80 1 2.5000000000000001E-03 2.4847632707043008E-07 2.8839964322800527E-07 5.5208680027618584E-07 6.6768099999999997E-01 6.6852699999999998E-01
The numbers are: number of grid points (HyPar::dim_global), number of processors (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.
Expected screen output:
HyPar - Parallel (MPI) version with 1 processes
Compiled with PETSc time integration.
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. : 400
Restart iteration : 0
Time integration scheme : PETSc
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 : 2.500000E-03
Check for conservation : no
Screen output iterations : 10
File output iterations : 40
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".
Setting up PETSc time integration...
SolvePETSc(): Problem type is nonlinear.
** Starting PETSc time integration **
0 TS dt 0.0025 time 0.
Writing solution file op_00000.dat.
1 TS dt 0.0025 time 0.0025
2 TS dt 0.0025 time 0.005
3 TS dt 0.0025 time 0.0075
4 TS dt 0.0025 time 0.01
5 TS dt 0.0025 time 0.0125
6 TS dt 0.0025 time 0.015
7 TS dt 0.0025 time 0.0175
8 TS dt 0.0025 time 0.02
9 TS dt 0.0025 time 0.0225
Iteration: 10 Time: 2.500E-02 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
10 TS dt 0.0025 time 0.025
11 TS dt 0.0025 time 0.0275
12 TS dt 0.0025 time 0.03
13 TS dt 0.0025 time 0.0325
14 TS dt 0.0025 time 0.035
15 TS dt 0.0025 time 0.0375
16 TS dt 0.0025 time 0.04
17 TS dt 0.0025 time 0.0425
18 TS dt 0.0025 time 0.045
19 TS dt 0.0025 time 0.0475
Iteration: 20 Time: 5.000E-02 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
20 TS dt 0.0025 time 0.05
21 TS dt 0.0025 time 0.0525
22 TS dt 0.0025 time 0.055
23 TS dt 0.0025 time 0.0575
24 TS dt 0.0025 time 0.06
25 TS dt 0.0025 time 0.0625
26 TS dt 0.0025 time 0.065
27 TS dt 0.0025 time 0.0675
28 TS dt 0.0025 time 0.07
29 TS dt 0.0025 time 0.0725
Iteration: 30 Time: 7.500E-02 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
30 TS dt 0.0025 time 0.075
31 TS dt 0.0025 time 0.0775
32 TS dt 0.0025 time 0.08
33 TS dt 0.0025 time 0.0825
34 TS dt 0.0025 time 0.085
35 TS dt 0.0025 time 0.0875
36 TS dt 0.0025 time 0.09
37 TS dt 0.0025 time 0.0925
38 TS dt 0.0025 time 0.095
39 TS dt 0.0025 time 0.0975
Iteration: 40 Time: 1.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00001.dat.
40 TS dt 0.0025 time 0.1
41 TS dt 0.0025 time 0.1025
42 TS dt 0.0025 time 0.105
43 TS dt 0.0025 time 0.1075
44 TS dt 0.0025 time 0.11
45 TS dt 0.0025 time 0.1125
46 TS dt 0.0025 time 0.115
47 TS dt 0.0025 time 0.1175
48 TS dt 0.0025 time 0.12
49 TS dt 0.0025 time 0.1225
Iteration: 50 Time: 1.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
50 TS dt 0.0025 time 0.125
51 TS dt 0.0025 time 0.1275
52 TS dt 0.0025 time 0.13
53 TS dt 0.0025 time 0.1325
54 TS dt 0.0025 time 0.135
55 TS dt 0.0025 time 0.1375
56 TS dt 0.0025 time 0.14
57 TS dt 0.0025 time 0.1425
58 TS dt 0.0025 time 0.145
59 TS dt 0.0025 time 0.1475
Iteration: 60 Time: 1.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
60 TS dt 0.0025 time 0.15
61 TS dt 0.0025 time 0.1525
62 TS dt 0.0025 time 0.155
63 TS dt 0.0025 time 0.1575
64 TS dt 0.0025 time 0.16
65 TS dt 0.0025 time 0.1625
66 TS dt 0.0025 time 0.165
67 TS dt 0.0025 time 0.1675
68 TS dt 0.0025 time 0.17
69 TS dt 0.0025 time 0.1725
Iteration: 70 Time: 1.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
70 TS dt 0.0025 time 0.175
71 TS dt 0.0025 time 0.1775
72 TS dt 0.0025 time 0.18
73 TS dt 0.0025 time 0.1825
74 TS dt 0.0025 time 0.185
75 TS dt 0.0025 time 0.1875
76 TS dt 0.0025 time 0.19
77 TS dt 0.0025 time 0.1925
78 TS dt 0.0025 time 0.195
79 TS dt 0.0025 time 0.1975
Iteration: 80 Time: 2.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00002.dat.
80 TS dt 0.0025 time 0.2
81 TS dt 0.0025 time 0.2025
82 TS dt 0.0025 time 0.205
83 TS dt 0.0025 time 0.2075
84 TS dt 0.0025 time 0.21
85 TS dt 0.0025 time 0.2125
86 TS dt 0.0025 time 0.215
87 TS dt 0.0025 time 0.2175
88 TS dt 0.0025 time 0.22
89 TS dt 0.0025 time 0.2225
Iteration: 90 Time: 2.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
90 TS dt 0.0025 time 0.225
91 TS dt 0.0025 time 0.2275
92 TS dt 0.0025 time 0.23
93 TS dt 0.0025 time 0.2325
94 TS dt 0.0025 time 0.235
95 TS dt 0.0025 time 0.2375
96 TS dt 0.0025 time 0.24
97 TS dt 0.0025 time 0.2425
98 TS dt 0.0025 time 0.245
99 TS dt 0.0025 time 0.2475
Iteration: 100 Time: 2.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
100 TS dt 0.0025 time 0.25
101 TS dt 0.0025 time 0.2525
102 TS dt 0.0025 time 0.255
103 TS dt 0.0025 time 0.2575
104 TS dt 0.0025 time 0.26
105 TS dt 0.0025 time 0.2625
106 TS dt 0.0025 time 0.265
107 TS dt 0.0025 time 0.2675
108 TS dt 0.0025 time 0.27
109 TS dt 0.0025 time 0.2725
Iteration: 110 Time: 2.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
110 TS dt 0.0025 time 0.275
111 TS dt 0.0025 time 0.2775
112 TS dt 0.0025 time 0.28
113 TS dt 0.0025 time 0.2825
114 TS dt 0.0025 time 0.285
115 TS dt 0.0025 time 0.2875
116 TS dt 0.0025 time 0.29
117 TS dt 0.0025 time 0.2925
118 TS dt 0.0025 time 0.295
119 TS dt 0.0025 time 0.2975
Iteration: 120 Time: 3.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00003.dat.
120 TS dt 0.0025 time 0.3
121 TS dt 0.0025 time 0.3025
122 TS dt 0.0025 time 0.305
123 TS dt 0.0025 time 0.3075
124 TS dt 0.0025 time 0.31
125 TS dt 0.0025 time 0.3125
126 TS dt 0.0025 time 0.315
127 TS dt 0.0025 time 0.3175
128 TS dt 0.0025 time 0.32
129 TS dt 0.0025 time 0.3225
Iteration: 130 Time: 3.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
130 TS dt 0.0025 time 0.325
131 TS dt 0.0025 time 0.3275
132 TS dt 0.0025 time 0.33
133 TS dt 0.0025 time 0.3325
134 TS dt 0.0025 time 0.335
135 TS dt 0.0025 time 0.3375
136 TS dt 0.0025 time 0.34
137 TS dt 0.0025 time 0.3425
138 TS dt 0.0025 time 0.345
139 TS dt 0.0025 time 0.3475
Iteration: 140 Time: 3.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
140 TS dt 0.0025 time 0.35
141 TS dt 0.0025 time 0.3525
142 TS dt 0.0025 time 0.355
143 TS dt 0.0025 time 0.3575
144 TS dt 0.0025 time 0.36
145 TS dt 0.0025 time 0.3625
146 TS dt 0.0025 time 0.365
147 TS dt 0.0025 time 0.3675
148 TS dt 0.0025 time 0.37
149 TS dt 0.0025 time 0.3725
Iteration: 150 Time: 3.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
150 TS dt 0.0025 time 0.375
151 TS dt 0.0025 time 0.3775
152 TS dt 0.0025 time 0.38
153 TS dt 0.0025 time 0.3825
154 TS dt 0.0025 time 0.385
155 TS dt 0.0025 time 0.3875
156 TS dt 0.0025 time 0.39
157 TS dt 0.0025 time 0.3925
158 TS dt 0.0025 time 0.395
159 TS dt 0.0025 time 0.3975
Iteration: 160 Time: 4.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00004.dat.
160 TS dt 0.0025 time 0.4
161 TS dt 0.0025 time 0.4025
162 TS dt 0.0025 time 0.405
163 TS dt 0.0025 time 0.4075
164 TS dt 0.0025 time 0.41
165 TS dt 0.0025 time 0.4125
166 TS dt 0.0025 time 0.415
167 TS dt 0.0025 time 0.4175
168 TS dt 0.0025 time 0.42
169 TS dt 0.0025 time 0.4225
Iteration: 170 Time: 4.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
170 TS dt 0.0025 time 0.425
171 TS dt 0.0025 time 0.4275
172 TS dt 0.0025 time 0.43
173 TS dt 0.0025 time 0.4325
174 TS dt 0.0025 time 0.435
175 TS dt 0.0025 time 0.4375
176 TS dt 0.0025 time 0.44
177 TS dt 0.0025 time 0.4425
178 TS dt 0.0025 time 0.445
179 TS dt 0.0025 time 0.4475
Iteration: 180 Time: 4.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
180 TS dt 0.0025 time 0.45
181 TS dt 0.0025 time 0.4525
182 TS dt 0.0025 time 0.455
183 TS dt 0.0025 time 0.4575
184 TS dt 0.0025 time 0.46
185 TS dt 0.0025 time 0.4625
186 TS dt 0.0025 time 0.465
187 TS dt 0.0025 time 0.4675
188 TS dt 0.0025 time 0.47
189 TS dt 0.0025 time 0.4725
Iteration: 190 Time: 4.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
190 TS dt 0.0025 time 0.475
191 TS dt 0.0025 time 0.4775
192 TS dt 0.0025 time 0.48
193 TS dt 0.0025 time 0.4825
194 TS dt 0.0025 time 0.485
195 TS dt 0.0025 time 0.4875
196 TS dt 0.0025 time 0.49
197 TS dt 0.0025 time 0.4925
198 TS dt 0.0025 time 0.495
199 TS dt 0.0025 time 0.4975
Iteration: 200 Time: 5.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00005.dat.
200 TS dt 0.0025 time 0.5
201 TS dt 0.0025 time 0.5025
202 TS dt 0.0025 time 0.505
203 TS dt 0.0025 time 0.5075
204 TS dt 0.0025 time 0.51
205 TS dt 0.0025 time 0.5125
206 TS dt 0.0025 time 0.515
207 TS dt 0.0025 time 0.5175
208 TS dt 0.0025 time 0.52
209 TS dt 0.0025 time 0.5225
Iteration: 210 Time: 5.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
210 TS dt 0.0025 time 0.525
211 TS dt 0.0025 time 0.5275
212 TS dt 0.0025 time 0.53
213 TS dt 0.0025 time 0.5325
214 TS dt 0.0025 time 0.535
215 TS dt 0.0025 time 0.5375
216 TS dt 0.0025 time 0.54
217 TS dt 0.0025 time 0.5425
218 TS dt 0.0025 time 0.545
219 TS dt 0.0025 time 0.5475
Iteration: 220 Time: 5.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
220 TS dt 0.0025 time 0.55
221 TS dt 0.0025 time 0.5525
222 TS dt 0.0025 time 0.555
223 TS dt 0.0025 time 0.5575
224 TS dt 0.0025 time 0.56
225 TS dt 0.0025 time 0.5625
226 TS dt 0.0025 time 0.565
227 TS dt 0.0025 time 0.5675
228 TS dt 0.0025 time 0.57
229 TS dt 0.0025 time 0.5725
Iteration: 230 Time: 5.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
230 TS dt 0.0025 time 0.575
231 TS dt 0.0025 time 0.5775
232 TS dt 0.0025 time 0.58
233 TS dt 0.0025 time 0.5825
234 TS dt 0.0025 time 0.585
235 TS dt 0.0025 time 0.5875
236 TS dt 0.0025 time 0.59
237 TS dt 0.0025 time 0.5925
238 TS dt 0.0025 time 0.595
239 TS dt 0.0025 time 0.5975
Iteration: 240 Time: 6.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00006.dat.
240 TS dt 0.0025 time 0.6
241 TS dt 0.0025 time 0.6025
242 TS dt 0.0025 time 0.605
243 TS dt 0.0025 time 0.6075
244 TS dt 0.0025 time 0.61
245 TS dt 0.0025 time 0.6125
246 TS dt 0.0025 time 0.615
247 TS dt 0.0025 time 0.6175
248 TS dt 0.0025 time 0.62
249 TS dt 0.0025 time 0.6225
Iteration: 250 Time: 6.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
250 TS dt 0.0025 time 0.625
251 TS dt 0.0025 time 0.6275
252 TS dt 0.0025 time 0.63
253 TS dt 0.0025 time 0.6325
254 TS dt 0.0025 time 0.635
255 TS dt 0.0025 time 0.6375
256 TS dt 0.0025 time 0.64
257 TS dt 0.0025 time 0.6425
258 TS dt 0.0025 time 0.645
259 TS dt 0.0025 time 0.6475
Iteration: 260 Time: 6.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
260 TS dt 0.0025 time 0.65
261 TS dt 0.0025 time 0.6525
262 TS dt 0.0025 time 0.655
263 TS dt 0.0025 time 0.6575
264 TS dt 0.0025 time 0.66
265 TS dt 0.0025 time 0.6625
266 TS dt 0.0025 time 0.665
267 TS dt 0.0025 time 0.6675
268 TS dt 0.0025 time 0.67
269 TS dt 0.0025 time 0.6725
Iteration: 270 Time: 6.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
270 TS dt 0.0025 time 0.675
271 TS dt 0.0025 time 0.6775
272 TS dt 0.0025 time 0.68
273 TS dt 0.0025 time 0.6825
274 TS dt 0.0025 time 0.685
275 TS dt 0.0025 time 0.6875
276 TS dt 0.0025 time 0.69
277 TS dt 0.0025 time 0.6925
278 TS dt 0.0025 time 0.695
279 TS dt 0.0025 time 0.6975
Iteration: 280 Time: 7.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00007.dat.
280 TS dt 0.0025 time 0.7
281 TS dt 0.0025 time 0.7025
282 TS dt 0.0025 time 0.705
283 TS dt 0.0025 time 0.7075
284 TS dt 0.0025 time 0.71
285 TS dt 0.0025 time 0.7125
286 TS dt 0.0025 time 0.715
287 TS dt 0.0025 time 0.7175
288 TS dt 0.0025 time 0.72
289 TS dt 0.0025 time 0.7225
Iteration: 290 Time: 7.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
290 TS dt 0.0025 time 0.725
291 TS dt 0.0025 time 0.7275
292 TS dt 0.0025 time 0.73
293 TS dt 0.0025 time 0.7325
294 TS dt 0.0025 time 0.735
295 TS dt 0.0025 time 0.7375
296 TS dt 0.0025 time 0.74
297 TS dt 0.0025 time 0.7425
298 TS dt 0.0025 time 0.745
299 TS dt 0.0025 time 0.7475
Iteration: 300 Time: 7.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
300 TS dt 0.0025 time 0.75
301 TS dt 0.0025 time 0.7525
302 TS dt 0.0025 time 0.755
303 TS dt 0.0025 time 0.7575
304 TS dt 0.0025 time 0.76
305 TS dt 0.0025 time 0.7625
306 TS dt 0.0025 time 0.765
307 TS dt 0.0025 time 0.7675
308 TS dt 0.0025 time 0.77
309 TS dt 0.0025 time 0.7725
Iteration: 310 Time: 7.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
310 TS dt 0.0025 time 0.775
311 TS dt 0.0025 time 0.7775
312 TS dt 0.0025 time 0.78
313 TS dt 0.0025 time 0.7825
314 TS dt 0.0025 time 0.785
315 TS dt 0.0025 time 0.7875
316 TS dt 0.0025 time 0.79
317 TS dt 0.0025 time 0.7925
318 TS dt 0.0025 time 0.795
319 TS dt 0.0025 time 0.7975
Iteration: 320 Time: 8.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00008.dat.
320 TS dt 0.0025 time 0.8
321 TS dt 0.0025 time 0.8025
322 TS dt 0.0025 time 0.805
323 TS dt 0.0025 time 0.8075
324 TS dt 0.0025 time 0.81
325 TS dt 0.0025 time 0.8125
326 TS dt 0.0025 time 0.815
327 TS dt 0.0025 time 0.8175
328 TS dt 0.0025 time 0.82
329 TS dt 0.0025 time 0.8225
Iteration: 330 Time: 8.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
330 TS dt 0.0025 time 0.825
331 TS dt 0.0025 time 0.8275
332 TS dt 0.0025 time 0.83
333 TS dt 0.0025 time 0.8325
334 TS dt 0.0025 time 0.835
335 TS dt 0.0025 time 0.8375
336 TS dt 0.0025 time 0.84
337 TS dt 0.0025 time 0.8425
338 TS dt 0.0025 time 0.845
339 TS dt 0.0025 time 0.8475
Iteration: 340 Time: 8.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
340 TS dt 0.0025 time 0.85
341 TS dt 0.0025 time 0.8525
342 TS dt 0.0025 time 0.855
343 TS dt 0.0025 time 0.8575
344 TS dt 0.0025 time 0.86
345 TS dt 0.0025 time 0.8625
346 TS dt 0.0025 time 0.865
347 TS dt 0.0025 time 0.8675
348 TS dt 0.0025 time 0.87
349 TS dt 0.0025 time 0.8725
Iteration: 350 Time: 8.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
350 TS dt 0.0025 time 0.875
351 TS dt 0.0025 time 0.8775
352 TS dt 0.0025 time 0.88
353 TS dt 0.0025 time 0.8825
354 TS dt 0.0025 time 0.885
355 TS dt 0.0025 time 0.8875
356 TS dt 0.0025 time 0.89
357 TS dt 0.0025 time 0.8925
358 TS dt 0.0025 time 0.895
359 TS dt 0.0025 time 0.8975
Iteration: 360 Time: 9.000E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00009.dat.
360 TS dt 0.0025 time 0.9
361 TS dt 0.0025 time 0.9025
362 TS dt 0.0025 time 0.905
363 TS dt 0.0025 time 0.9075
364 TS dt 0.0025 time 0.91
365 TS dt 0.0025 time 0.9125
366 TS dt 0.0025 time 0.915
367 TS dt 0.0025 time 0.9175
368 TS dt 0.0025 time 0.92
369 TS dt 0.0025 time 0.9225
Iteration: 370 Time: 9.250E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
370 TS dt 0.0025 time 0.925
371 TS dt 0.0025 time 0.9275
372 TS dt 0.0025 time 0.93
373 TS dt 0.0025 time 0.9325
374 TS dt 0.0025 time 0.935
375 TS dt 0.0025 time 0.9375
376 TS dt 0.0025 time 0.94
377 TS dt 0.0025 time 0.9425
378 TS dt 0.0025 time 0.945
379 TS dt 0.0025 time 0.9475
Iteration: 380 Time: 9.500E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
380 TS dt 0.0025 time 0.95
381 TS dt 0.0025 time 0.9525
382 TS dt 0.0025 time 0.955
383 TS dt 0.0025 time 0.9575
384 TS dt 0.0025 time 0.96
385 TS dt 0.0025 time 0.9625
386 TS dt 0.0025 time 0.965
387 TS dt 0.0025 time 0.9675
388 TS dt 0.0025 time 0.97
389 TS dt 0.0025 time 0.9725
Iteration: 390 Time: 9.750E-01 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
390 TS dt 0.0025 time 0.975
391 TS dt 0.0025 time 0.9775
392 TS dt 0.0025 time 0.98
393 TS dt 0.0025 time 0.9825
394 TS dt 0.0025 time 0.985
395 TS dt 0.0025 time 0.9875
396 TS dt 0.0025 time 0.99
397 TS dt 0.0025 time 0.9925
398 TS dt 0.0025 time 0.995
399 TS dt 0.0025 time 0.9975
Iteration: 400 Time: 1.000E+00 Max CFL: 2.000E-01 Max Diff. No.: 0.000E+00
Writing solution file op_00010.dat.
400 TS dt 0.0025 time 1.
** Completed PETSc time integration **
Reading array from ASCII file exact.inp (Serial mode).
Computed errors:
L1 Error : 2.4847632707043008E-07
L2 Error : 2.8839964322800527E-07
Linfinity Error : 5.5208680027618584E-07
Conservation Errors:
0.0000000000000000E+00
Solver runtime (in seconds): 6.6768099999999997E-01
Total runtime (in seconds): 6.6852699999999998E-01
Deallocating arrays.
Finished.