We use the exact solution of a stationary rotating vortex for 2D Euler equations as initial conditions and to quantify the error in the density in the L1 norm. This specific exact solution is available under VortexRotationExactSolution. The computational codes are available here: [Clawpack], [WENO]
For the following tests we use the computational domain [0,1]x[0.1] and the parameters
The ghost fluid boundary is a circle around with radius and rotates by itself with velocity .We access the accuracy of the Ghost-fluid method implemented generically in AMROC for the
First test with reflecting slip wall boundary conditions at the imbedded boundary:
N | Wave Propagation | Godunov-Splitting | WENO - 7 Pt | ||||||
Error | Order | Mass loss | Error | Order | Mass loss | Error | Order | Mass loss | |
20 | 1.729e-05 | -9.136e-07 | 3.718e-05 | -7.567e-07 | 3.232e-05 | 6.297e-06 | |||
40 | 1.646e-05 | 0.07 | -5.025e-08 | 1.736e-05 | 1.10 | -3.570e-08 | 2.024e-05 | 0.68 | -2.086e-08 |
80 | 5.595e-06 | 1.56 | -2.383e-09 | 5.702e-06 | 1.61 | -1.190e-09 | 5.919e-06 | 1.77 | -3.122e-10 |
160 | 1.472e-06 | 1.93 | -1.343e-10 | 1.399e-06 | 2.03 | -9.116e-11 |
Second test with extrapolation boundary conditions at the imbedded boundary:
N | Wave Propagation | Godunov-Splitting | WENO - 7 Pt | ||||||
Error | Order | Mass loss | Error | Order | Mass loss | Error | Order | Mass loss | |
20 | 5.970e-05 | -8.862e-07 | 4.491e-05 | -1.105e-06 | 0.0001210 | 5.108e-05 | |||
40 | 2.571e-05 | 1.22 | -4.916e-08 | 1.766e-05 | 1.35 | -4.630e-08 | 1.574e-05 | 2.94 | -4.361e-08 |
80 | 3.316e-06 | 2.95 | -2.402e-09 | 3.697e-06 | 2.26 | -2.103e-09 | 4.358e-06 | 1.85 | -1.821e-09 |
160 | 1.168e-06 | 1.51 | -1.359e-10 | 1.176e-06 | 1.65 | -1.098e-10 |
N | Wave Propagation | Godunov-Splitting | WENO - 7 Pt | ||||||
Error | Order | Mass loss | Error | Order | Mass loss | Error | Order | Mass loss | |
20 | 0.0120056 | 0.0079236 | 0.0144203 | 0.0020241 | 0.0064736 | 0.0028641 | |||
40 | 0.0035074 | 1.78 | 0.0011898 | 0.0073070 | 0.98 | 0.0001300 | 0.0017008 | 1.93 | 0.0004790 |
80 | 0.0014193 | 1.31 | 0.0001588 | 0.0038401 | 0.93 | -0.0001036 | 0.0006816 | 1.32 | -5.878e-05 |
160 | 0.0005032 | 1.50 | 5.046e-05 | 0.0018988 | 1.02 | -2.783e-06 |
First test with reflecting slip wall boundary conditions at the imbedded boundary:
N | Wave Propagation | Godunov-Splitting | WENO - 7 Pt | ||||||
Error | Order | Mass loss | Error | Order | Mass loss | Error | Order | Mass loss | |
20 | 0.0423925 | 0.0423925 | 0.0271446 | 0.0271446 | 0.0260747 | 0.0260747 | |||
40 | 0.0358735 | 0.24 | 0.0358735 | 0.0242260 | 0.16 | 0.0242260 | 0.0236603 | 0.14 | 0.0236603 |
80 | 0.0212340 | 0.76 | 0.0212340 | 0.0128638 | 0.91 | 0.0128638 | 0.0128931 | 0.88 | 0.0128931 |
160 | 0.0121089 | 0.81 | 0.0121089 | 0.0070906 | 0.86 | 0.0070906 |
Second test with extrapolation boundary conditions at the imbedded boundary:
N | Wave Propagation | Godunov-Splitting | WENO - 7 Pt | ||||||
Error | Order | Mass loss | Error | Order | Mass loss | Error | Order | Mass loss | |
20 | 0.0575232 | 0.0575232 | 0.0512302 | 0.0512302 | 0.0376556 | 0.0376556 | |||
40 | 0.0479454 | 0.26 | 0.0479454 | 0.0417552 | 0.30 | 0.0417552 | 0.0303673 | 0.31 | 0.0303673 |
80 | 0.0327630 | 0.55 | 0.0327630 | 0.0272841 | 0.61 | 0.0272841 | 0.0196045 | 0.63 | 0.0196045 |
160 | 0.0206183 | 0.67 | 0.0206183 | 0.0166053 | 0.72 | 0.0166053 |
-- RalfDeiterding - 23 Feb 2005
I | Attachment | Size | Date | Who | Comment |
---|---|---|---|---|---|
VelocWaveProp.mpg | 1733.9 K | 01 Mar 2005 - 05:57 | RalfDeiterding | Development of length of velocity vector for Wave Propagation |