Sign Preserving WENO-AO-type Central Upwind Schemes

doi:10.19596/j.cnki.1001-246x.8507

Abstract

Abstract:

In this paper we give a sufficient condition for sign preservation in Weighted Essentially Non-Oscillatory with Adaptive Order (WENO-AO) reconstruction, which means to keep same sign for jumping at interfaces. WENO-AO reconstruction realizes self-adaptive accuracy through an nonlinear combination of high-order polynomial and low-order reconstruction. In solving solution near discontinuous points, WENO-AO reconstruction is more accurate than the classical WENO reconstruction, and it keeps good stability. The scheme is obtained by combining a central upwind numerical flux with a third-order strongly stable Runge-Kutta method. Numerical results show that the scheme has fifth order accuracy. It has characteristics of high resolution and strong robustness. It captures accurately discontinuous positions and avoids effectively the generation of spurious oscillation.

Key words: sign preserving, WENO-AO reconstruction, hyperbolic conservation laws equations, central upwind flux function

Supei ZHENG, Mangmang JIAN, Jianhu FENG, Mengqing ZHAI. Sign Preserving WENO-AO-type Central Upwind Schemes[J]. Chinese Journal of Computational Physics, 2022, 39(6): 677-686.

Figures/Tables 9

References 24

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N	L₁ error	Rate	L_∞ error	Rate
40	2.237 9 × 10^-6		4.678 7 × 10^-6
80	6.025 7 × 10^-8	5.21	1.248 4 × 10^-7	5.22
160	1.730 5 × 10^-9	5.12	3.630 2 × 10^-9	5.10
320	5.168 8 × 10^-11	5.06	1.108 9 × 10^-10	5.03
640	1.578 3 × 10^-12	5.03	3.427 9 × 10^-12	5.01

N	L₁ error	Rate	L_∞ error	Rate
40	2.237 9 × 10^-6		4.678 7 × 10^-6
80	6.025 7 × 10^-8	5.21	1.248 4 × 10^-7	5.22
160	1.730 5 × 10^-9	5.12	3.630 2 × 10^-9	5.10
320	5.168 8 × 10^-11	5.06	1.108 9 × 10^-10	5.03
640	1.578 3 × 10^-12	5.03	3.427 9 × 10^-12	5.01

N	WENO-AO		WENO5
N	L_∞ error	Rate	L_∞ error	Rate
20	2.680 1 × 10^-4		2.700 0 × 10^-3
40	6.382 7 × 10^-6	5.39	3.845 7 × 10^-4	2.81
80	1.703 4 × 10^-7	5.23	6.128 9 × 10^-5	2.65
160	4.952 5 × 10^-9	5.10	8.089 5 × 10^-6	2.92
320	1.514 0 × 10^-10	5.03	1.024 3 × 10^-6	2.98

N	WENO-AO		WENO5
N	L_∞ error	Rate	L_∞ error	Rate
20	2.680 1 × 10^-4		2.700 0 × 10^-3
40	6.382 7 × 10^-6	5.39	3.845 7 × 10^-4	2.81
80	1.703 4 × 10^-7	5.23	6.128 9 × 10^-5	2.65
160	4.952 5 × 10^-9	5.10	8.089 5 × 10^-6	2.92
320	1.514 0 × 10^-10	5.03	1.024 3 × 10^-6	2.98

N	L₁ error	Rate	L_∞ error	Rate
20	1.367 3 × 10^-4		1.839 4 × 10^-5
40	5.071 8 × 10^-6	4.75	6.035 5 × 10^-7	4.93
80	1.770 1 × 10^-7	4.84	1.886 4 × 10^-8	4.99
160	5.706 3 × 10^-9	4.96	5.900 7 × 10^-10	5.00
320	1.796 2 × 10^-10	4.99	1.845 1 × 10^-11	5.00