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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

Dongwook Lee Open the ORCID record for Dongwook Lee [Opens in a new window]  and
Rémi Bourgeois
Dongwook Lee
Affiliation:
Department of Applied Mathematics, The University of California, Santa Cruz, CA, United States, email:dlee79@ucsc.edu
Rémi Bourgeois
Affiliation:
Maison de la Simulation, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France, email:remi.bourgeois@cea.fr
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Abstract

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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.

Keywords

Gaussian Process modelingMOOD methodhigh-order methodfinite volume methoda posteriori detectionpositivity-preserving method
Type
Contributed Paper
Information
Proceedings of the International Astronomical Union , Volume 16 , Symposium S362: The Predictive Power of Computational Astrophysics as a Discovery Tool , June 2020 , pp. 373 - 379
Creative Commons
Creative Common License - CCCreative Common License - BY
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.
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of International Astronomical Union

References

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