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ADAPTIVE METHODS

Here we want demonstrate the asset of adaptive methods for the inviscid flow through GAMM channel. We have developed two adaptive strategies:

  • multilevel mesh refinement ([1]) based on the shock indicator, which seeks the physically admissible shock waves

  • anisotropic mesh adaptation ([2]) which construct completely new mesh in the sense that the interpolation error is uniformly distributed over the whole computational domain

    Both of these method are applied for the flow through GAMM channel and they are compared with the results obtained without local mesh adaptation. There exist a shock wave for inlet Mach number M_{int} = 0.67. The shock wave is a discontinuity but in numerical realisation it is only a jump of quantity with a very high gradient. Our aim was to obtain for all three method results with high quality, which is meassured as the magnitute of gradient of Mach number on shock wave.

    Computational results

    Method number of elements CPU times gradient of shock waves Links to results
    global refinement 108 240 21 600 s 69.5 GLOBAL
    multlevel mesh refinement 2 813 240 s 535.5 MMR
    anisotropic mesh adptation 2 470 780 s 298.1 AMA

    This table shows that apllying adaptive strategies (AMA or MMR) we have results of higher quality (higher gradient) than for global refinement. Also the CPU-time and number of elements was multiple smaller. All three strategies captured the Zierepp singularity (local minimum behind the shock wave).

    Global mesh refinement

    The triangulation and isolines of Mach number.
    Some details of results are available     here.

    Multilevel mesh refinement

    The triangulation and isolines of Mach number.
    Some details of results are available     here.

    Anisotropic mesh adaptation

    The triangulation and isolines of Mach number.
    Some details of results are available     here.

    The summary results are available here.

    Bibliography

    [1] J.Felcman and V.Dolejsi: Adaptive Methods in Internal and External Flow Computations. In M.Brons, M.P.Bendsoe and M.P.Sorensen, editors, Progress in Industrial Mathematics at ECMI 96, pages 424-431, B.G.Teubner, Stuttgart, 1997. ISBN 3-519-02607-4

    [2] V. Dolejsi: Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes. Computing and Visualisation in Science (to appear).