A Hybrid Targeted Eno-Thinc Scheme With a Modified BVD Algorithm and its Application in Stiff Detonation

Abstract

This paper presents a new hybrid scheme which combines the fifth-order Targeted Essentially Non-Oscillatory (TENO) reconstruction and the tangent of hyperbola for interface capturing (THINC) reconstruction by using a modified boundary variation diminishing (MBVD) algorithm to select one of the two candidate reconstructions. The THINC scheme has a jump-like distribution can approximate a discontinuity well within a mesh cell with high fidelity. The original BVD algorithm is based on minimisation of jumps of reconstructed variables at cell interfaces in order to reduce the dissipation in numerical flux. The present MBVD algorithm minimises the dissipation terms of the HLL flux which includes jumps of both variables and fluxes at cell interfaces. A number of benchmark examples demonstrate that the MBVD algorithm is more robust than the original BVD algorithm. Applications in stiff detonation problems show that the present hybrid scheme can capture detonation fronts better than the single TENO scheme.