Theory and Modern Applications
From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model
Δ t | \(\boldsymbol {\|{\mathbf{u}}_{3.3}^{m,\Delta t}-{\mathbf{u}}_{3.3}^{m,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},\Delta t,0}}\) | \(\boldsymbol {\|{\mathbf{u}}_{3.3}^{m,\Delta t}-{\mathbf{u}}_{3.3}^{m,\frac{\Delta t}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},\Delta t,1}}\) | \(\boldsymbol {\|p_{3.3}^{m,\Delta t}-p_{3.3}^{m,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{p_{f},\Delta t,0}}\) |
---|---|---|---|---|---|---|
0.1 | 0.00090236 | 1.93382 | 0.00891485 | 1.85837 | 0.0215839 | 1.89965 |
0.05 | 0.00046662 | 1.96917 | 0.00479714 | 2.00887 | 0.011362 | 1.95491 |
0.025 | 0.000236963 | 1.98516 | 0.00238798 | 1.68501 | 0.00581205 | 1.97876 |
0.0125 | 0.000119368 | 0.00141719 | 0.00293722 |
Δ t | \(\boldsymbol {\|\phi_{3.3}^{m,\Delta t}-\phi_{3.3}^{m,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{\phi,\Delta t,0}}\) | \(\boldsymbol {\|\phi_{3.3}^{m,\Delta t}-\phi_{3.3}^{m,\frac{\Delta t}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{\phi,\Delta t,1}}\) |
---|---|---|---|---|
0.1 | 0.00433364 | 1.90828 | 0.0174115 | 1.88974 |
0.05 | 0.00227097 | 1.95936 | 0.00921372 | 1.94985 |
0.025 | 0.00115904 | 1.98099 | 0.00472534 | 1.92982 |
0.0125 | 0.00058508 | 0.00244859 |