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Point value multiscale algorithms for 2D compressible flows
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DOI：10.1137/S1064827599363988.png)
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The numerical simulation of physical problems modeled by systems of conservation laws is di cult due to the presence of discontinuities in the solution. High-order shock capturing schemes combine sharp numerical profiles at discontinuities with a highly accurate approximation in smooth regions, but usually their computational cost is quite large. Following the idea of A. Harten [Comm. Pure Appl. Math., 48 (1995), pp. 1305-1342] and Bihari and Harten [SIAM J. Sci. Comput., 18 (1997), pp. 315-354], we present in this paper a method to reduce the execution time of such simulations. It is based on a point value multiresolution transform that is used to detect regions with singularities. In these regions, an expensive high-resolution shock capturing scheme is applied to compute the numerical flux at cell interfaces. In smooth regions a cheap polynomial interpolation is used to deduce the value of the numerical divergence from values previously obtained on lower resolution scales. This method is applied to solve the two-dimensional compressible Euler equations for two classical configurations. The results are analyzed in terms of quality and efficiency.
Keyword:
conservation laws
multiresolution
shock capturing schemes
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2.6
论文数:
5.1K
被引数:
1.8W
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