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This paper introduces a novel approach to compute the numerical fluxes at thecell boundaries in the finite volume approach. Explicit gradients used inderiving the reconstruction polynomials are replaced by high-order gradientscomputed by compact finite differences, referred to as implicit gradients inthis paper. The new finite volume scheme has superior dispersion anddissipation properties in comparison to the compact reconstruction approach.These implicit gradients are re-used in viscous flux computation andpost-processing, which further improves efficiency. A problem-independent shockcapturing approach via Boundary Variation Diminishing (BVD) algorithm is usedto suppress oscillations for the simulation of flows with shocks and materialinterfaces. Several numerical test cases are carried out to verify the proposedfinite volume method's capability using the implicit gradient method for singleand multicomponent flows. Significant improvements are observed by computingthe gradients implicitly for the viscous flows.

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