A high resolution total variation diminishing scheme for hyperbolic conservation law and related problems

A high resolution, explicit second order accurate, total variation diminishing (TVD) difference scheme using flux limiter approach for scalar hyperbolic conservation law and closely related convectively dominated diffusion problem is presented. Bounds and TVD region is given for these limiters such that the resulting scheme is TVD. A class of such limiters is given which gives second order accurate TVD scheme. Numerical results for one-dimensional scalar conservation law and convectively dominated diffusion problem are presented. Comparison of numerical results with some of the classical difference schemes are given.