An accurate finite-volume formulation of a Residual-Based Compact scheme for unsteady compressible flows

Abstract The paper discusses the design principles of a Finite-Volume Residual-Based Compact (RBC) scheme for the spatial discretization of the unsteady compressible governing equations of gas dynamics on general structured meshes. Our goal is to develop an accurate and robust approximation methodology, well suited for complex problems of industrial interest. The scheme makes use of weighted approximations that allow to ensure high accuracy while taking benefit from the structured nature of the grid. The accuracy and Cauchy stability properties of the proposed spatial approximation are discussed in detail. Numerical applications to unsteady compressible flows of increasing complexity demonstrate the advantages of the proposed formulation with respect to straightforward extensions of RBC schemes to curvilinear meshes.

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