An efficient invariant-region-preserving central scheme for hyperbolic conservation laws

• Published in: Applied mathematics and computation 2023-01, Vol.436, p.127500, Article 127500
• Main Authors: Yan, Ruifang, Tong, Wei, Chen, Guoxian
• Format: Article
• Language: English
• Subjects: Forward-backward splitting; Hyperbolic conservation laws; Invariant-region-preserving principle; Minimum-maximum-preserving principle; Positivity-preserving principle; Unstaggered-central scheme
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127500

•New second-order accurate invariant-region-preserving(IRP) unstaggered-central scheme for the hyperbolic conservation laws.•Extended IRP limiter, which is applied to reconstructed slopes such that it remains effective in the vicinity of the active cell.•Proof of stability, which is so called froward-backward splitting, is adaptable for scalar equations and general nonlinear systems.•More relaxed CFL condition implies the larger time step. Due to the Riemann solver free and avoiding characteristic decomposition, the central scheme is a simple and efficient tool for numerical solution of hyperbolic conservation laws (Nessyahu and Tadmor, J. Comput. Phys., 87(2):314-329,1990). But the theoretical Courant number CFL in order to preserve the invariant region of the numerical solution is very small, and there is lack of the stability proof for nonlinear systems. By adding a limiter on the reconstructed slope without requiring clipping condition, we enlarge the value of the CFL to admit larger time step. Then a widely applicable stability proof, which is suitable for general hyperbolic conservation laws, is given by writing the evolved solution as convex combinations in terms of the Lax-Friedrichs scheme. Some numerical experiments are carried out to verify the robustness.