19 January 2020 11:30:34 AM
FD1D_BURGERS_LAX:
C version
Solve the non-viscous time-dependent Burgers equation,
using the Lax-Wendroff method.
Equation to be solved:
du/dt + u * du/dx = 0
for x in [ a, b ], for t in [t_init, t_last]
with initial conditions:
u(x,o) = u_init
and boundary conditions:
u(a,t) = u_a(t), u(b,t) = u_b(t)
-1.000000 <= X <= 1.000000
Number of nodes = 41
DX = 0.050000
0.000000 <= T <= 1.000000
Number of time steps = 80
DT = 0.012500
X:
-1.000000 -0.950000 -0.900000 -0.850000 -0.800000 -0.750000
-0.750000 -0.700000 -0.650000 -0.600000 -0.550000 -0.500000
-0.500000 -0.450000 -0.400000 -0.350000 -0.300000 -0.250000
-0.250000 -0.200000 -0.150000 -0.100000 -0.050000 0.000000
0.000000 0.050000 0.100000 0.150000 0.200000 0.250000
0.250000 0.300000 0.350000 0.400000 0.450000 0.500000
0.500000 0.550000 0.600000 0.650000 0.700000 0.750000
0.750000 0.800000 0.850000 0.900000 0.950000 1.000000
1.000000
STEP = 0
TIME = 0.000000
STABILITY = 0.125000
0.500000 0.483680 0.466525 0.448495 0.429553
0.409666 0.388800 0.366932 0.344042 0.320120
0.295167 0.269197 0.242238 0.214334 0.185547
0.155958 0.125666 0.094786 0.063451 0.031805
0.000000 -0.031805 -0.063451 -0.094786 -0.125666
-0.155958 -0.185547 -0.214334 -0.242238 -0.269197
-0.295167 -0.320120 -0.344042 -0.366932 -0.388800
-0.409666 -0.429553 -0.448495 -0.466525 -0.483680
-0.500000
STEP = 1
TIME = 0.012500
STABILITY = 0.125000
0.500000 0.491773 0.474730 0.456785 0.437893
0.418014 0.397110 0.375146 0.352098 0.327947
0.302688 0.276327 0.248889 0.220416 0.190969
0.160634 0.129515 0.097739 0.065452 0.032815
-0.000000 -0.032815 -0.065452 -0.097739 -0.129515
-0.160634 -0.190969 -0.220416 -0.248889 -0.276327
-0.302688 -0.327947 -0.352098 -0.375146 -0.397110
-0.418014 -0.437893 -0.456785 -0.474730 -0.491773
-0.500000
STEP = 2
TIME = 0.025000
STABILITY = 0.125000
0.500000 0.497809 0.483033 0.465196 0.446381
0.426538 0.405622 0.383591 0.360410 0.336053
0.310505 0.283766 0.255853 0.226805 0.196683
0.165575 0.133592 0.100874 0.067580 0.033890
-0.000000 -0.033890 -0.067580 -0.100874 -0.133592
-0.165575 -0.196683 -0.226805 -0.255853 -0.283766
-0.310505 -0.336053 -0.360410 -0.383591 -0.405622
-0.426538 -0.446381 -0.465196 -0.483033 -0.497809
-0.500000
STEP = 3
TIME = 0.037500
STABILITY = 0.125448
0.500000 0.501791 0.490856 0.473719 0.455007
0.435230 0.414332 0.392264 0.368979 0.344442
0.318627 0.291524 0.263145 0.233520 0.202710
0.170803 0.137919 0.104207 0.069846 0.035037
-0.000000 -0.035037 -0.069846 -0.104207 -0.137919
-0.170803 -0.202710 -0.233520 -0.263145 -0.291524
-0.318627 -0.344442 -0.368979 -0.392264 -0.414332
-0.435230 -0.455007 -0.473719 -0.490856 -0.501791
-0.500000
STEP = 4
TIME = 0.050000
STABILITY = 0.125965
0.500000 0.503859 0.497621 0.482193 0.463761
0.444079 0.423232 0.401159 0.377802 0.353115
0.327060 0.299615 0.270781 0.240581 0.209072
0.176342 0.142516 0.107757 0.072264 0.036262
-0.000000 -0.036262 -0.072264 -0.107757 -0.142516
-0.176342 -0.209072 -0.240581 -0.270781 -0.299615
-0.327060 -0.353115 -0.377802 -0.401159 -0.423232
-0.444079 -0.463761 -0.482193 -0.497621 -0.503859
-0.500000
STEP = 5
TIME = 0.062500
STABILITY = 0.126073
0.500000 0.504294 0.502829 0.490305 0.472591
0.453075 0.432312 0.410269 0.386877 0.362074
0.335810 0.308048 0.278776 0.248008 0.215791
0.182214 0.147407 0.111546 0.074849 0.037573
-0.000000 -0.037573 -0.074849 -0.111546 -0.147407
-0.182214 -0.215791 -0.248008 -0.278776 -0.308048
-0.335810 -0.362074 -0.386877 -0.410269 -0.432312
-0.453075 -0.472591 -0.490305 -0.502829 -0.504294
-0.500000
STEP = 6
TIME = 0.075000
STABILITY = 0.126534
0.500000 0.503494 0.506137 0.497615 0.481367
0.462194 0.441561 0.419587 0.396198 0.371318
0.344881 0.316834 0.287147 0.255821 0.222893
0.188447 0.152618 0.115595 0.077620 0.038980
-0.000000 -0.038980 -0.077620 -0.115595 -0.152618
-0.188447 -0.222893 -0.255821 -0.287147 -0.316834
-0.344881 -0.371318 -0.396198 -0.419587 -0.441561
-0.462194 -0.481367 -0.497615 -0.506137 -0.503494
-0.500000
STEP = 7
TIME = 0.087500
STABILITY = 0.126858
0.500000 0.501937 0.507432 0.503621 0.489843
0.471382 0.450962 0.429099 0.405756 0.380843
0.354274 0.325979 0.295907 0.264040 0.230403
0.195070 0.158179 0.119931 0.080594 0.040494
-0.000000 -0.040494 -0.080594 -0.119931 -0.158179
-0.195070 -0.230403 -0.264040 -0.295907 -0.325979
-0.354274 -0.380843 -0.405756 -0.429099 -0.450962
-0.471382 -0.489843 -0.503621 -0.507432 -0.501937
-0.500000
STEP = 8
TIME = 0.100000
STABILITY = 0.126964
0.500000 0.500123 0.506861 0.507855 0.497647
0.480521 0.460488 0.438791 0.415540 0.390641
0.363989 0.335489 0.305069 0.272687 0.238348
0.202115 0.164122 0.124584 0.083796 0.042126
-0.000000 -0.042126 -0.083796 -0.124584 -0.164122
-0.202115 -0.238348 -0.272687 -0.305069 -0.335489
-0.363989 -0.390641 -0.415540 -0.438791 -0.460488
-0.480521 -0.497647 -0.507855 -0.506861 -0.500123
-0.500000
STEP = 9
TIME = 0.112500
STABILITY = 0.127498
0.500000 0.498500 0.504822 0.509991 0.504306
0.489401 0.470082 0.448644 0.425537 0.400704