Advances in Applied Mathematics and Mechanics (Adv. Appl. Math. Mech.) (20220101), 14, no.~5, 1181-1200. ISSN: 2070-0733 (print).eISSN: 2075-1354.
Subject
65 Numerical analysis -- 65M Partial differential equations, initial value and time-dependent initial-boundary value problems 65M12 Stability and convergence of numerical methods
Summary: ``It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors. In this paper, a well-balanced weighted compact nonlinear scheme (WCNS) is proposed for shallow water equations in pre-balanced forms. The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term. Some numerical examples in one-and two-dimensions are also presented to demonstrate the well-balanced property, high order accuracy and good shock capturing capability of the proposed scheme.''