Adaptive Central-Upwind Schemes for Hy- perbolic Systems of Conservation Laws

Abstract. Central-upwind schemes, recently introduced in [7, 8], are simple, universal, and ecient Godunov-type projection-evolution methods for hyperbolic systems of conservation laws. Their eciency, however, is typically reduced at the projection step, which requires nonlinear limiters to prevent oscillations. Such limiters, especially those that are higher than second order accu-rate, are computationally expensive. They may also cause exces-sive smearing of (liner) contact waves. We present a new adaptive version of the central-upwind schemes, in which second-order limiters are applied near shock waves only, while in the rest of the computational domain, an unlimited fth-order reconstruction is employed. Our adaption strategy is based on the modied version of the weak local residual from [5], which is used to automatically distinguish between shock and contact discontinuities. 1