Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T08:00:37.783Z Has data issue: false hasContentIssue false
  • English
  • Français

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:[email protected]
Rémi Bourgeois
Affiliation:
Maison de la Simulation, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France, email:[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Reyes, A., Lee, D., Graziani, C., and Tzeferacos, P.. Journal of Scientific Computing, 76:0 443–480, 2018 a. ISSN 0885-7474. doi: 10.1007/s10915-017-0625-2 CrossRefGoogle Scholar
Adam Reyes, Dongwook Lee, Graziani, Carlo, and Tzeferacos, Petros. Journal of Computational Physics, 381:0 189–217, 2019.CrossRefGoogle Scholar
Steve Reeves, Dongwook Lee, Reyes, Adam, Graziani, Carlo, and Tzeferacos, Petros. arXiv preprint arXiv:2003.08508; Accepted for publication in CAMCoS, 2021.Google Scholar
Bourgeois, Rémi and Lee, Dongwook. Journal of Computational Physics, 471:111603, 2022.CrossRefGoogle Scholar
James Kent, Christiane Jablonowski, Jared P Whitehead, and Richard B Rood. Journal of Computational Physics, 278:0 497–508, 2014.Google Scholar
Clain, Stéphane, Diot, Steven, and Loubère, Raphaël. Journal of Computational Physics, 2300 (10):0 4028–4050, 2011.CrossRefGoogle Scholar
Diot, Steven, Clain, Stéphane, and Loubère, Raphaël. Computers & Fluids, 64:0 43–63, 2012.CrossRefGoogle Scholar
Diot, Steven, Loubère, Raphaël, and Clain, Stephane. International Journal for Numerical Methods in Fluids, 730 (4):0 362–392, 2013.CrossRefGoogle Scholar
Diot, Steven. PhD thesis, Université de Toulouse, Université Toulouse III-Paul Sabatier, 2012.Google Scholar
Adam Reyes, Dongwook Lee, Graziani, Carlo, and Tzeferacos, Petros. Journal of Scientific Computing, 760 (1):0 443–480, 2018 b.Google Scholar
Shu, Chi-Wang. In Advanced numerical approximation of nonlinear hyperbolic equations, pages 325–432. Springer, 1998.CrossRefGoogle Scholar
Chi-Wang, Shu and Osher, Stanley. In Upwind and High-Resolution Schemes, pages 328–374. Springer, 1989. Google Scholar