High-order central-upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) algorithm

A total variation diminishing high resolution scheme for nonlinear conservation laws

In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total varia...

A Genuinely High Order Total Variation Diminishing Scheme for One-Dimensional Scalar Conservation Laws

It is well known that finite difference or finite volume total variation diminishing (TVD) schemes solving one-dimensional scalar conservation laws degenerate to first order accuracy at smooth extrema [8], thus TVD schemes are at most second order accurate in the L1 norm for general smooth and non-monotone solutions. However, Sanders [12] introduced a third order accurate finite volume scheme w...

High-Order Shock Capturing for Computational Aeroacoustics

Simulation of Hypersonic Shock Wave/Boundary Layer Interaction Using High Order WENO Scheme

This paper investigates the accuracy and robustness of high order WENO schemes for predicting hypersonic shock wave/boundary layer interaction. The implicit time marching method with unfactored Gauss-Seidel line relaxation is used with a 5th order WENO finite difference scheme for inviscid fluxes. The viscous terms are discretized using a 4th order conservative central differencing. Numerical r...

High-order central-upwind schemes for hyperbolic conservation laws

We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [A. Kurganov, S. Noelle and G. Petrova, SIAM J. Sci. Comput., 23 (2001), pp. 707–740]. Similarly to the staggered central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality, and robustness. At the sam...