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Asymptotic-preserving schemes for multiscale physical problems

Published online by Cambridge University Press:  09 June 2022

Shi Jin
Shi Jin*
Affiliation:
School of Mathematical Sciences, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China E-mail: shijin-m@sjtu.edu.cn
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Abstract

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We present the asymptotic transitions from microscopic to macroscopic physics, their computational challenges and the asymptotic-preserving (AP) strategies to compute multiscale physical problems efficiently. Specifically, we will first study the asymptotic transition from quantum to classical mechanics, from classical mechanics to kinetic theory, and then from kinetic theory to hydrodynamics. We then review some representative AP schemes that mimic these asymptotic transitions at the discrete level, and hence can be used crossing scales and, in particular, capture the macroscopic behaviour without resolving the microscopic physical scale numerically.

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Type
Research Article
Information
Acta Numerica , Volume 31 , May 2022 , pp. 415 - 489
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 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© Shanghai Jiao Tong University, 2022. Published by Cambridge University Press

Footnotes

*

S. Jin was partially supported by National Key R&D Program of China Project no. 2020YFA0712000, NSFC grant no. 12031013, Strategic Priority Research Program of Chinese Academy of Sciences XDA25010401, and Shanghai Municipal Science and Technology Major Project 2021SHZDZX0102.

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