Abstract. 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 ...

2.1 Examples of conservative schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Godunov Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 The Lax-Friedrichs Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 The local Lax-Friedrichs Scheme . . . . . . . ....

In this paper we present the MmB schemes, which preserve the local maximum and minimum bounds of the initial data in the smallest union of mesh elements of previous time step containing the domain of dependence of the solution on the mesh element with center at point P under consideration. In 1-D, the MmB schemes are almost identical with TVD schemes. As well-known, there is no second-order TVD...

We present a pedagogical review of some of the methods employed in Eulerian computational fluid dynamics (CFD). Fluid mechanics is governed by the Euler equations, which are conservation laws for mass, momentum, and energy. The standard approach to Eulerian CFD is to divide space into finite volumes or cells and store the cell-averaged values of conserved hydro quantities. The integral Euler eq...

A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying conventional TVD schemes moment transport equations. In present method, a realizable set at cell face reconstructed by allowing flexible selection limiter values within region. Necessary conditions for scheme s...