Table 1 Accuracy test: errors and convergence orders at \(t=2\) obtained by linear compact GKS on regular tetrahedral meshes
From: High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh
Scheme | \(h_{re}\) | \(Error_{L^1}\) | \(\mathcal {O}_{L^1}\) | \(Error_{L^{\infty }}\) | \(\mathcal {O}_{L^{\infty }}\) |
|---|---|---|---|---|---|
2nd-order compact GKS | \(10^3\times 6\) | 2.0826e-02 | Â | 3.3425e-02 | Â |
\(20^3\times 6\) | 5.5685e-03 | 1.90 | 8.7536e-03 | 1.93 | |
\(40^3\times 6\) | 1.4054e-03 | 1.99 | 2.2178e-03 | 1.98 | |
\(50^3\times 6\) | 8.9934e-04 | 2.00 | 2.2178e-03 | 2.00 | |
3rd-order compact GKS | \(10^3\times 6\) | 2.6059e-03 | Â | 4.9418e-03 | Â |
\(20^3\times 6\) | 2.4874e-04 | 3.39 | 4.8530e-04 | 3.35 | |
\(40^3\times 6\) | 2.7360e-05 | 3.18 | 5.3194e-05 | 3.19 | |
\(50^3\times 6\) | 1.3751e-05 | 3.08 | 2.6821e-05 | 3.07 | |
4th-order compact GKS | \(10^3\times 6\) | 4.8439e-04 | Â | 9.2211e-04 | Â |
\(20^3\times 6\) | 2.7104e-05 | 4.16 | 6.7724e-05 | 3.77 | |
\(40^3\times 6\) | 1.6770e-06 | 4.01 | 6.3761e-06 | 3.41 | |
\(50^3\times 6\) | 6.9290e-07 | 3.96 | 2.9498e-06 | 3.45 |