High-Resolution Nonoscillatory Central Schemes with Nonstaggered Grids for Hyperbolic Conservation Laws

. We present a general procedure to convert schemes which are based on staggered spatial grids into non-staggered schemes. This procedure is then utilized to construct a new family of non-staggered, central schemes for hyperbolic conservation laws, by converting the family of staggered central schemes recently introduced in [22, 21, 9]. These new nonstaggered central schemes retain the desirable properties of simplicity and high-resolution, and in particular, they yield Riemann-solver-free recipes which avoid dimensional splitting. Most importantly, the new central schemes avoid staggered grids and hence are simpler to implement in frameworks which involve complex geometries and boundary conditions. AMS(MOS) subject classification. Primary 65M10; Secondary 65M05 Keywords. Hyperbolic conservation laws, central schemes, staggered grids. Contents 1 Introduction 2 2 Motivation: the First-Order Lax-Friedrichs (LxF) Scheme 3 3 One-Dimensional Extensions to Higher-Orders 5 3.1 The second-...