A viscous flux formulation at interior faces and at Dirichlet boundary conditions in the framework of unstructured vertex-centered k -exact finite-volume schemes is presented. It is based on a geometric decomposition of the viscous flux into orthogonal and nonorthogonal parts. Special emphasis is put on the truncation errors and the spectral properties of the scheme, and a connection is established to the well-known α -damping scheme. The latter is also used to introduce discretization coefficients into the method that allow a fourth and a sixth order of accuracy in space on Cartesian grids. The effect of the scheme is presented in terms of canonical diffusion problems, as well as test cases for laminar wall-bounded flows. It is shown that the method preserves a second-order accuracy for the viscous operator, even on highly distorted unstructured grids and in the presence of boundaries and that it strongly enhances the solution accuracy with respect to a conventional scheme for viscous fluxes.


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    Title :

    Investigating a High-Order Viscous Flux Scheme for Unstructured Grids


    Contributors:

    Published in:

    AIAA Journal ; 62 , 12 ; 4798-4811


    Publication date :

    2024-12-01




    Type of media :

    Conference paper , Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English






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