Theory and Modern Applications
From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model
Δ t | \(\boldsymbol {\|{\mathbf{u}}_{3.2}^{m,\Delta t}-{\mathbf{u}}_{3.2}^{m,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},\Delta t,0}}\) | \(\boldsymbol {\|{\mathbf{u}}_{3.2}^{m,\Delta t}-{\mathbf{u}}_{3.2}^{m,\frac{\Delta t}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},\Delta t,1}}\) | \(\boldsymbol {\|p_{3.2}^{m,\Delta t}-p_{3.2}^{m,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{p_{f},\Delta t,0}}\) |
---|---|---|---|---|---|---|
0.1 | 0.000809376 | 1.95487 | 0.0080253 | 1.86026 | 0.0173397 | 1.9429 |
0.05 | 0.000414031 | 1.97844 | 0.00431408 | 2.02706 | 0.00892463 | 1.97378 |
0.025 | 0.000209272 | 1.98947 | 0.00212825 | 1.62937 | 0.00452159 | 1.98749 |
0.0125 | 0.00010519 | 0.00130618 | 0.00227502 |
Δ t | \(\boldsymbol {\|\phi_{3.2}^{m,h\Delta t}-\phi_{3.2}^{m,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{\phi,\Delta t,0}}\) | \(\boldsymbol {\|\phi_{3.2}^{m,\Delta t}-\phi_{3.2}^{m,\frac{\Delta t}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{\phi,\Delta t,1}}\) |
---|---|---|---|---|
0.1 | 0.00257197 | 1.92495 | 0.0140113 | 1.89193 |
0.05 | 0.00133612 | 1.96705 | 0.00740581 | 1.94972 |
0.025 | 0.000679251 | 1.98468 | 0.0037984 | 1.90576 |
0.0125 | 0.000342248 | 0.00199312 |