High Order Asymptotic Preserving and Well-Balanced Schemes for the Shallow Water Equations with Source Terms
Year: 2024
Author: Guanlan Huang, Sebastiano Boscarino, Tao Xiong
Communications in Computational Physics, Vol. 35 (2024), Iss. 5 : pp. 1229–1262
Abstract
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual purpose: firstly, preserving all steady states within the model, and secondly, maintaining the late-time asymptotic behavior of solutions, which is governed by a diffusion equation and coincides with a long time and stiff friction limit.
Our proposed approach draws inspiration from a penalization technique adopted in [Boscarino et al., SIAM Journal on Scientific Computing, 2014]. By employing an additive implicit-explicit Runge-Kutta method, the scheme can ensure a correct asymptotic behavior for the limiting diffusion equation, without suffering from a parabolic-type time step restriction which often afflicts multiscale problems in the diffusive limit. Numerical experiments are performed to illustrate high order accuracy, asymptotic preserving, and asymptotically accurate properties of the designed schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0274
Communications in Computational Physics, Vol. 35 (2024), Iss. 5 : pp. 1229–1262
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Shallow water equations Manning friction asymptotic preserving well-balanced implicit-explicit Runge-Kutta high order.