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Compressible Flow SUPG Stabilization Parameters Computed from Degree-of-freedom Submatrices

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Abstract

We present, for the SUPG formulation of inviscid compressible flows, stabilization parameters defined based on the degree-of-freedom submatrices of the element-level matrices. With 2D steady-state test problems involving supersonic flows and shocks, we compare these stabilization parameters with the ones defined based on the full element-level matrices. We also compare them to the stabilization parameters introduced in the earlier development stages of the SUPG formulation of compressible flows. In all cases the formulation includes a shock-capturing term involving a shock-capturing parameter. We investigate the difference between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every nonlinear iteration within a time step. The formulation includes, as an option, an algorithmic feature that is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected.

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Authors and Affiliations

  1. Department of Computer Science, Federal University of Espírito Santo (UFES), Av. Fernando Ferrari, 514, Goiabeiras, 29075-910, Vitória, Brazil

    Lucia Catabriga

  2. Department of Civil Engineering - COPPE, Federal University of Rio de Janeiro (UFRJ), Caixa Postal, 68506, Rio de Janeiro, Brazil

    Alvaro L. G. A. Coutinho

  3. Team for Advanced Flow Simulation and Modeling (T*AFSM), Mechanical Engineering, Rice University - MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Tayfun E. Tezduyar

Authors
  1. Lucia Catabriga
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  2. Alvaro L. G. A. Coutinho
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  3. Tayfun E. Tezduyar
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Correspondence to Alvaro L. G. A. Coutinho.

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Catabriga, L., Coutinho, A.L.G.A. & Tezduyar, T.E. Compressible Flow SUPG Stabilization Parameters Computed from Degree-of-freedom Submatrices. Comput Mech 38, 334–343 (2006). https://doi.org/10.1007/s00466-006-0033-1

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  • DOI: https://doi.org/10.1007/s00466-006-0033-1

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