Volume 12, Issue 6
A High-Order Well-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model

Jiaojiao Li, Gang Li, Shouguo Qian, Jinmei Gao & Qiang Niu

Adv. Appl. Math. Mech., 12 (2020), pp. 1416-1437.

Published online: 2020-09

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  • Abstract

In this work, we present a high-order discontinuous Galerkin method for the shallow water equations incorporating horizontal temperature gradients (also known as the Ripa model), which exactly maintains the lake at rest steady state. Herein, we propose original numerical fluxes defined on the basis of the hydrostatic reconstruction idea and a simple source term approximation. This novel approach allows us to achieve the well-balancing of the discontinuous Galerkin method without complication. Moreover, the proposed method retains genuinely high-order accuracy for smooth solutions and it shows good resolution for discontinuous solutions at the same time. Rigorous numerical analysis as well as extensive numerical results all verify the good performances of the proposed method.

  • Keywords

Ripa model, lake at rest steady state, source term, discontinuous Galerkin method, well-balancing property, hydrostatic reconstruction.

  • AMS Subject Headings

74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1416, author = {Li , Jiaojiao and Li , Gang and Qian , Shouguo and Gao , Jinmei and Niu , Qiang}, title = {A High-Order Well-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {6}, pages = {1416--1437}, abstract = {

In this work, we present a high-order discontinuous Galerkin method for the shallow water equations incorporating horizontal temperature gradients (also known as the Ripa model), which exactly maintains the lake at rest steady state. Herein, we propose original numerical fluxes defined on the basis of the hydrostatic reconstruction idea and a simple source term approximation. This novel approach allows us to achieve the well-balancing of the discontinuous Galerkin method without complication. Moreover, the proposed method retains genuinely high-order accuracy for smooth solutions and it shows good resolution for discontinuous solutions at the same time. Rigorous numerical analysis as well as extensive numerical results all verify the good performances of the proposed method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0220}, url = {http://global-sci.org/intro/article_detail/aamm/18294.html} }
TY - JOUR T1 - A High-Order Well-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model AU - Li , Jiaojiao AU - Li , Gang AU - Qian , Shouguo AU - Gao , Jinmei AU - Niu , Qiang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1416 EP - 1437 PY - 2020 DA - 2020/09 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0220 UR - https://global-sci.org/intro/article_detail/aamm/18294.html KW - Ripa model, lake at rest steady state, source term, discontinuous Galerkin method, well-balancing property, hydrostatic reconstruction. AB -

In this work, we present a high-order discontinuous Galerkin method for the shallow water equations incorporating horizontal temperature gradients (also known as the Ripa model), which exactly maintains the lake at rest steady state. Herein, we propose original numerical fluxes defined on the basis of the hydrostatic reconstruction idea and a simple source term approximation. This novel approach allows us to achieve the well-balancing of the discontinuous Galerkin method without complication. Moreover, the proposed method retains genuinely high-order accuracy for smooth solutions and it shows good resolution for discontinuous solutions at the same time. Rigorous numerical analysis as well as extensive numerical results all verify the good performances of the proposed method.

Jiaojiao Li, Gang Li, Shouguo Qian, Jinmei Gao & Qiang Niu. (2020). A High-Order Well-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model. Advances in Applied Mathematics and Mechanics. 12 (6). 1416-1437. doi:10.4208/aamm.OA-2019-0220
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