A general method for building multidimensional shape preserving advection schemes using flux limiters is presented. The method part of the intervening space. The flux form is a conservation works for advected passive scalars in either compressible or incomlaw in the sense of theoretical physics. One corollary is that pressible flow and on arbitrary grids. With a minor modification it the total amount of the advected substance, ΝqdV, is not can be applied to the equation for fluid density. Schemes using the changed by the advection (given suitable boundary conditions).
simplest form of the flux limiter can cause distortion of the advected
The advective form states that the mixing ratio does not profile, particularly sideways spreading, depending on the orientation of the flow relative to the grid. This is partly because the change following a fluid parcel. This implies that extrema in simple limiter is too restrictive. However, some straightforward the mixing ratio distribution are not amplified. For brevity, this refinements lead to a shape-preserving scheme that gives satisfacwill be referred to as the shape preservation property. Two tory results, with negligible grid-flow angle-dependent distorcorollaries of this are (i) that a spatially homogeneous mixing tion.