Implicit gradients based conservative numerical scheme for compressible flows

Abstract

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. 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. 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 method's capability using the implicit gradient method for compressible flows.

arXiv admin note: substantial text overlap with arXiv:2106.01738

References in corpus (4)

• High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm
• Gradient Based Reconstruction: Inviscid and viscous flux discretizations, shock capturing, and its application to single and multicomponent flows
• Economically High-Order Unstructured-Grid Methods: Clarification and Efficient FSR Schemes
• On False Accuracy Verification of UMUSCL Scheme

Cited by in corpus (3)

• Wave or Physics-Appropriate Multidimensional Upwinding Approach for Compressible Multiphase Flows
• Consistent Interface Capturing Adaptive Reconstruction Approach for Viscous Compressible Multicomponent Flows
• Wave-appropriate reconstruction of compressible flows: physics-constrained acoustic dissipation and rank-1 entropy wave correction