A high-order non-oscillatory central scheme with non-staggered grids for hyperbolic conservation laws

Abstract

In this work, we present a scheme which is based on non-staggered grids. This scheme is a new family of non-staggered central schemes for hyperbolic conservation laws. Motivation of this work is a staggered central scheme recently introduced by A.A.I. Peer et al. [A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws, Appl. Numer. Math. 58 (2008) 674–688]. The most important properties of the technique developed in the current paper are simplicity, high-resolution and avoiding the use of staggered grids and hence is simpler to implement in frameworks which involve complex geometries and boundary conditions. Numerical implementation of the new scheme is carried out on the scalar conservation laws with linear, non-linear flux and systems of hyperbolic conservation laws. The numerical results confirm the expected accuracy and high-resolution properties of the scheme.