Table 4 Accuracy test for adaptive IMEX-RK-LDG scheme of 3D NS equations
k | N | \(\phantom {\dot {i}\!}\|\rho - \rho _{h}\|_{L^{2}}\) | Order | \(\phantom {\dot {i}\!}\|\mathbf {u}-\mathbf {u}_{h}\|_{L^{2}}\) | Order | \(\phantom {\dot {i}\!}\|p-p_{h}\|_{L^{2}}\) | Order |
|---|---|---|---|---|---|---|---|
1 | 4 | 1.76E-01 | – | 2.37E-01 | – | 1.50E-01 | – |
8 | 4.61E-02 | 1.93 | 6.37E-02 | 1.90 | 3.49E-02 | 2.10 | |
16 | 9.07E-03 | 2.34 | 1.34E-02 | 2.25 | 6.77E-03 | 2.37 | |
32 | 1.81E-03 | 2.31 | 3.00E-03 | 2.15 | 1.44E-03 | 2.23 | |
2 | 4 | 5.00E-02 | – | 7.46E-02 | – | 4.70E-02 | – |
8 | 7.73E-03 | 2.69 | 1.02E-02 | 2.86 | 6.35E-03 | 2.88 | |
16 | 8.06E-04 | 3.26 | 1.16E-03 | 3.13 | 7.35E-04 | 3.11 | |
32 | 9.26E-05 | 3.12 | 1.40E-04 | 3.05 | 8.98E-05 | 3.03 |