Central WENO schemes for hyperbolic systems of conservation laws. (English) Zbl 0938.65110

Levy, Doron; Puppo, Gabriella; Russo, Giovanni

M2AN, Math. Model. Numer. Anal. 33, No. 3, 547-571 (1999).

A family of high order, essentially non-oscillatory, central schemes for approximating solutions of systems of hyperbolic conservation laws is presented. These schemes are based on a new centered version of the weighted essentially nonoscillatory (WENO) reconstruction of point-values from cell-averages, which is then followed by an accurate approximation of the fluxes via a natural continuous extension of Runge-Kutta solvers. Third- and fourth-order schemes are constructed and their high-resolution properties in several numerical tests are demonstrated.

Reviewer: L.G.Vulkov (Russe)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws

Keywords:

systems of hyperbolic conservation laws; numerical examples; Runge-Kutta methods; central weighted essentially non-oscillatory difference schemes