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 - <p style="text-align: justify;">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.</p>