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GP-MOOD: a positivity-preserving high-order finite volume method for hyperbolic conservation laws
Published online by Cambridge University Press: 20 January 2023
Abstract
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.
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- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of International Astronomical Union
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