From: The Euler implicit/explicit scheme for the Boussinesq equations
Δ t | \(\boldsymbol {\|u^{n,\Delta t}-u^{n,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{u,\Delta t,0}}\) | \(\boldsymbol {\|u^{n,\Delta t}-u^{n,\frac{\Delta t}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{u,\Delta t,1}}\) | \(\boldsymbol {\|p^{n,\Delta t}-p^{n,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{p,\Delta t,0}}\) |
---|---|---|---|---|---|---|
0.1 | 1.09819e−005 | 2.06348 | 7.97307e−005 | 2.06314 | 2.09931e−005 | 2.0025 |
0.05 | 5.32202e−006 | 2.04257 | 3.86453e−005 | 2.03837 | 1.04834e−005 | 1.64187 |
0.025 | 2.60556e−006 | 2.01799 | 1.89589e−005 | 1.91156 | 6.38507e−006 | 0.618958 |
0.0125 | 1.29116e−006 | 9.91804e−006 | 1.03158e−005 |
Δ t | \(\boldsymbol {\|\theta^{n,\Delta t}-\theta^{n,\frac{\Delta t}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{\theta,\Delta t,0}}\) | \(\boldsymbol {\|\theta^{n,\Delta t}-\theta^{n,\frac{\Delta t}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{\theta,\Delta t,1}}\) |
---|---|---|---|---|
0.1 | 1.14663e−005 | 2.06739 | 8.10132e−005 | 2.06742 |
0.05 | 5.54628e−006 | 2.03617 | 3.91857e−005 | 2.03617 |
0.025 | 2.72388e−006 | 2.01728 | 1.92448e−005 | 2.01729 |
0.0125 | 1.35028e−006 | 9.53992e−006 |