Implicit Gradients Based Conservative Numerical Scheme for Compressible Flows

This paper introduces a novel approach to compute the numerical fluxes at cell boundaries for cell-centered conservative scheme. Explicit gradients used in deriving reconstruction polynomials are replaced by high-order computed compact finite differences, referred as implicit this paper. A problem-independent shock capturing via Boundary Variation Diminishing (BVD) algorithm is suppress oscillations simulation of flows with shocks and material interfaces. Several test cases carried out verify proposed method’s capability using gradient method compressible flows.