Finite Volume Formulation of a Third-Order Residual-Based Compact Scheme for Unsteady Flow Computations

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. The scheme makes use of weighted approximations that allow to ensure high accuracy while taking benefit from the structured nature of the grid. The stability properties of the proposed spatial approximation are discussed. Numerical applications to unsteady compressible flows demonstrate the advantages of the proposed formulation with respect to straightforward extensions of RBC schemes.