A Class of High Resolution Shock Capturing Schemes for Non-linear Hyperbolic Conservation Laws

A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented. In the present work the numerical flux function for space discretization is constructed as a combination of numerical flux function of any entropy satisfying first order accurate scheme and second order accurate upstream scheme using the flux limiter function. The obtained high resolution schemes are shown to be TVD for 1-D scalar case. Bounds for the limiter function are given. Numerical experiments for various test problems clearly show that the resulting schemes give entropy consistent solution with higher resolution as compared to their corresponding first order schemes.