High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws

The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is explored and bounds derived for such limiters. A class of limiters is presented which includes a very compressive limiter due to Roe, and various limiters are compared both theoretically and numerically.