A new diffusion-regulated flux splitting method for compressible flows

Abstract

An improved version of a Low-Diffusion-Flux-Splitting (LDFS) scheme is presented. The original scheme was robust and accurate, especially in capturing strong shocks. However, the present studies reveal that a scope exists to improve the accuracy of the scheme to capture weak shocks. In order to meet this objective, the new methodology introduced in the present work imparts the LDFS scheme with the capability to crisply capture shocks and contact discontinuities irrespective of their strengths or grid inclinations. This multidimensional-like effect is imparted to the original scheme by first converting its upwind formulation to a central scheme with an artificial-viscosity term, followed by regulating the numerical diffusion using a Diffusion Regulation (DR) parameter and a shock switch. To the best of the authors’ knowledge this is the first successful attempt to apply this DR model with a shock switch to a Flux-Vector-Splitting scheme. The switch acts as the parameter for deciding where to locally activate or deactivate the diffusion regulation. The present innovation is found to significantly improve the shock-capturing accuracies of the parent scheme, especially for grid inclined weak shocks. Simultaneously it ensures that the new scheme is as robust as the parent scheme, especially in resolving strong shocks. The merits of the new methodology are clearly shown with the help of a number of carefully chosen inviscid and viscous test cases at a wide range of Mach numbers.