Implicit gradients based novel finite volume scheme for compressible single and multi-component flows

TL;DR

This paper presents a novel finite volume scheme for compressible flows that employs high-order implicit gradients for improved accuracy and efficiency, especially in flows with shocks and interfaces.

Contribution

The paper introduces a new finite volume method using implicit gradients computed by compact finite differences, enhancing dispersion, dissipation, and efficiency in compressible flow simulations.

Findings

Improved dispersion and dissipation properties over traditional methods.

Enhanced accuracy in viscous flow simulations with implicit gradients.

Effective shock capturing with Boundary Variation Diminishing algorithm.

Abstract

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. The new finite volume scheme has superior dispersion and dissipation properties in comparison to the compact reconstruction approach. These implicit gradients are re-used in viscous flux computation and post-processing, which further improves efficiency. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed finite volume method's capability using the implicit gradient method for single and multicomponent flows. Significant improvements are observed by computing the gradients implicitly for the viscous flows.