Multidimensional Flux-Limited Advection Schemes

A general method for building multidimensional shape preserving advection schemes using flux limiters is presented. The method works for advected passive scalars in either compressible or incompressible flow and on arbitrary grids. With a minor modification it can be applied to the equation for fluid density. Schemes using the simplest form of the flux limiter can cause distortion of the advected profile, particularly sideways spreading, depending on the orientation of the flow relative to the grid. This is partly because the simple limiter is too restrictive. However, some straightforward refinements lead to a shape-preserving scheme that gives satisfactory results, with negligible grid-flow angle-dependent distortion