High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm

TL;DR

This paper introduces a hybrid high-order shock-capturing scheme using a boundary variation diminishing algorithm that adaptively combines central and monotone schemes for improved resolution of flow features and discontinuities.

Contribution

It proposes a novel hybrid nonlinear explicit-compact scheme employing BVD for adaptive scheme selection, enhancing shock capturing and resolution of small-scale features.

Findings

Capable of resolving small-scale flow features.

Effective in capturing sharp discontinuities.

Comparable or improved performance over existing schemes.

Abstract

In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order possible interpolation, which is central, i.e. non-dissipative in the current approach and for the discontinuities, the algorithm selects the monotone scheme. This method provides an alternative to the existing adaptive upwind-central schemes in the literature. Several numerical examples are conducted with the present approach, which suggests that the current method is capable of resolving small scale flow features and has the same ability to capture sharp discontinuities as the MP5 scheme.