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1 results

  • GP-MOOD: a positivity-preserving high-order finite volume method for hyperbolic conservation laws

  • Dongwook Lee, Rémi Bourgeois
  • Journal:
    Proceedings of the International Astronomical Union / Volume 16 / Issue S362 / June 2020
    Published online by Cambridge University Press:
    20 January 2023, pp. 373-379
    Print publication:
    June 2020
    • Article
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  • We present an a posteriori shock-capturing finite volume method algorithm called GP-MOOD. The method solves a compressible hyperbolic conservative system at high-order solution accuracy in multiple spatial dimensions. The core design principle in GP-MOOD is to combine two recent numerical methods, the polynomial-free spatial reconstruction methods of GP (Gaussian Process) and the a posteriori detection algorithms of MOOD (Multidimensional Optimal Order Detection). We focus on extending GP’s flexible variability of spatial accuracy to an a posteriori detection formalism based on the MOOD approach. The resulting GP-MOOD method is a positivity-preserving method that delivers its solutions at high-order accuracy, selectable among three accuracy choices, including third-order, fifth-order, and seventh-order.