Construction of explicit and implicit symmetric tvd schemes and their applications
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
A class of implicit upwind schemes for Euler simulations with unstructured meshes
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
A second-order accurate, component-wise TVD scheme for nonlinear, hyperbolic conservation laws
Journal of Computational Physics
Positive schemes for solving multi-dimensional hyperbolic systems of conservation laws II
Journal of Computational Physics
Hi-index | 31.45 |
More robust developments of schemes for hyperbolic systems, that avoid dependence upon a characteristic decomposition have been achieved by employing schemes that are based on a Rusanov flux. Such schemes permit the construction of higher order approximations without recourse to characteristic decomposition. This is achieved by using the maximum eigenvalue of the hyperbolic system within the definition of the numerical flux. In recent literature the Rusanov flux has been embedded in a local Lax-Friedrichs flux. The current literature on these schemes only appears to indicate success in this regard, with no investigation of the effect of the additional numerical diffusion that is inherent in such formulations.In this paper the foundation for a new scheme is proposed which relies on the detection of the dominant wave in the system. This scheme is designed to permit the construction of lower and higher order approximations without recourse to characteristic decomposition while avoiding the excessive numerical diffusion that is inherent in the Rusanov and local Lax-Friedrichs fluxes.