This paper considers the performance of various shock-capturing schemes when simulating three-dimensional, hypersonic flows using the nodal discontinuous Galerkin (DG) finite element method on unstructured, hexahedral meshes. Simulations use a new code, Cartablanca++, which is verified using the method of manufactured solutions. Three shock-capturing techniques are compared: artificial viscosity (AV), slope limiting, and subcell finite volume limiting. Three test cases are considered, including a shock tube (one-dimensional), a reflecting shock (two-dimensional), and an inclined cylinder with a hemispherical endcap (three-dimensional). The AV formulation was not robust in the sense that it could not maintain pressure positivity after initialization from freestream conditions in the final three-dimensional test case. The slope and subcell limiters performed well in all simulations. Both techniques robustly captured strong shock waves while still benefiting from the use of high-order polynomials. The targeted application of the slope limiter prevented residual convergence to machine precision, while the subcell limiter could achieve residual convergence. The mixed DG/finite volume formulation, inherent to the subcell limiting scheme, appears sensitive to the inviscid flux function. Future work will consider modifications to reduce this sensitivity. Additionally, modifications to the shock detection techniques would improve performance for both the slope and subcell limiters.


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    Title :

    Comparing Discontinuous Galerkin Shock-Capturing Techniques Applied to Inviscid Three-Dimensional Hypersonic Flows


    Contributors:

    Published in:

    Publication date :

    2024-11-01




    Type of media :

    Conference paper , Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




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