Flux limiters

It is well known that first order accurate difference schemes for the numerical solution of conservation laws produce results which suffer from excessive numerical diffusion, classical second order schemes, although giving better resolution, suffer from spurious oscillations. Recently much effect has been put into achieving high resolution without these oscillations, using a variety of techniques. Here one class of such methods, that of flux limiting, is outlined together with the TVD constraint used to ensure oscillation free solutions. Brief numerical comparisons of different limiting functions are also presented.