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High-resolution Non-oscillatory Central Schemes with Non-staggered Grids for Hyperbolic Conservation Laws Dedicated to Our Friend and Colleague

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 non-staggered 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.