The Koren upwind scheme for variable gridsize Original Research Article

In this paper we derive a variable gridsize version of the Koren upwind scheme which is accurate when the gridsize changes in a non-smooth manner. We propose three different limiter functions to ensure monotonicity of the solution, and discuss the accuracy of these limiters. Numerical results are presented for linear and nonlinear advection in 1D as well as linear advection in 2D. The results show that the proposed scheme works satisfactorily even for abrupt grid changes.