A new TVD-MUSCL scheme for hyperbolic conservation laws

The second-order extension of Godunovʹs method for hyperbolic conservation laws, known as MUSCL schemes, is studied in this paper. We present a new type of Eulerian MUSCL scheme and oscillation-free algorithms. The intercell flux is computed from difference approximations of characteristic equations with the data influencing the values at half-time step. The data for characteristic equations are classified in several different types by the domain of dependence. The oscillation-free algorithm, based on TVD method, gives a general formulation for previously used method and provides a class of limiters including existing limiters. To validate the new TVD-MUSCL scheme, numerical experiments are performed for several model problems in one and two dimensions.