A general approach to enhance slope limiters on non-uniform grids

A general approach to study and enhance the slope limiter functions on non-uniform grids is presented. Slope limiters are preferred in high-resolutions schemes in general and MUSCL in particular to solve hyperbolic conservation laws. However, most 1D limiters are developed assuming uniform meshes in space, which are shown to be inadequate on non-uniform grids. Especially, secondorder convergence is shown to be lost when the conventional limiters are applied on irregular grids in the case of smooth solutions. A methodology based on the classical reconstruct-evolve-project approach and Harten’s stability theory is presented to study the slope limiters on 1D non-uniform computational grids. Sufficient conditions for the limiters to lead to formal second-order spatial accuracy, total-variational-diminishing stability and symmetry-preserving property are derived. The analysis and results extend naturally to cell-centered finite volume methods in multiple dimensions. Several most widely used conventional limiters are enhanced to satisfy these conditions, and their performances are illustrated by various 1D and 2D numerical examples.