TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

This data set contains the data accompanying the article F. Denner and B. van Wachem, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, Journal of Computational Physics (2015), http://dx.doi.org/10.1016/j.jcp.2015.06.008.This data set contains the data accompanying the article F. Denner and B. van Wachem, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, Journal of Computational Physics (2015), http://dx.doi.org/10.1016/j.jcp.2015.06.008

On the implementation of a class of upwind schemes for system of hyperbolic conservation laws

The relative computational effort among the spatially five point numerical flux functions of Harten, van Leer, and Osher and Chakravarthy is explored. These three methods typify the design principles most often used in constructing higher than first order upwind total variation diminishing (TVD) schemes. For the scalar case the difference in operation count between any two algorithms may be very small and yet the operation count for their system counterparts might be vastly different. The situation occurs even though one starts with two different yet equivalent representations for the scalar case

Numerical experiments with a symmetric high-resolution shock-capturing scheme

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use

On the convergence of difference approximations to scalar conservation laws

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality