Two variants of the MCV3 scheme

TL;DR

This paper introduces two improved variants of the MCV3 scheme based on flux reconstruction, enhancing accuracy, stability, and implementation simplicity for multi-dimensional problems.

Contribution

The paper presents two novel MCV3 variants that improve accuracy, stability, and ease of implementation without solving derivative Riemann problems.

Findings

Higher numerical accuracy than original MCV3

Less restrictive CFL condition for stability

Simplified implementation in arbitrary 2D and 3D meshes

Abstract

Two variants of the MCV3 scheme are presented based on a flux reconstruction formulation. Different from the original multi-moment constrained finite volume method of third order (MCV3), the multi-moment constraints are imposed at the cell center on the point value, the first and second order derivatives. The continuity of the flux function at cell interfaces are also used as the constraints to ensure the numerical conservation. Compared to the original MCV3 scheme, both two variants have higher numerical accuracy and less restrictive CFL condition for computational stability. Moreover, without the need to solve derivative Riemann problem at cell boundaries, the new schemes benefit the implementations in arbitrary quadrilateral in 2D and hexahedron in 3D.