Galerkin finite element methods for the Shallow Water equations over variable bottom

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:373

Article; Proceedings Paper

Kounadis, G.^1,2  Dougalis, V. A.^1,2 

[1] Natl & Kapodistrian Univ Athens, Dept Math, Zografos 15784, Greece

[2] FORTH, Inst Appl & Computat Math, Iraklion 70013, Greece

关键词: Shallow water equations;    Standard Galerkin finite element method;    Error estimates;    Characteristic boundary conditions;    Variable bottom topography;   

DOI  :  10.1016/j.cam.2019.06.031

来源: Elsevier

【 摘 要 】

We consider the one-dimensional shallow water equations (SW) in a finite channel with variable bottom topography. We pose several initial-boundary-value problems for the SW system, including problems with transparent (characteristic) boundary conditions in the supercritical and the subcritical case. We discretize these problems in the spatial variable by standard Galerkin-finite element methods and prove L-2-error estimates for the resulting semidiscrete approximations. We couple the schemes with the 4th order-accurate, explicit, classical Runge-Kutta time stepping procedure and use the resulting fully discrete methods in numerical experiments of shallow water wave propagation over variable bottom topographies with several kinds of boundary conditions. We discuss issues related to the attainment of a steady state of the simulated flows, including the good balance of the schemes. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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