An efficient finite difference method for the shallow water equations

被引：16
|
作者：
Lundgren, Lukas [1 ]
Mattsson, Ken [1 ]
机构：
[1] Uppsala Univ, Dept Informat Technol, POB 337, S-75105 Uppsala, Sweden
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 422卷
关键词：
Finite difference methods; Shallow water equations; High-order accuracy; Stability; Boundary treatment; Well-balanced; CENTRAL-UPWIND SCHEME; DISCONTINUOUS GALERKIN METHOD; NAVIER-STOKES EQUATIONS; ARTIFICIAL VISCOSITY; BOUNDARY-CONDITIONS; CURVILINEAR MESHES; NUMERICAL-SOLUTION; PARTS OPERATORS; EULER EQUATIONS; FAR-FIELD;
D O I：
10.1016/j.jcp.2020.109784
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A high-order explicit finite difference scheme is derived solving the shallow water equations. The boundary closures are based on the diagonal-norm summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique. Flux-splitting combined with upwind SBP operators is used to naturally introduce artificial dissipation. The scheme is tested against various benchmark problems where high-order convergence is verified for smooth solutions. A particular discretization of the source term is used leading to a well-balanced scheme. We also present an application: A simplified incident wave simulation with wave-channel interaction using a multi-block setup. Experiments suggest that a bathymetry consisting of many spikes could provide a dispersing effect on an incoming wave. (C) 2020 Elsevier Inc. All rights reserved.
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页数：28
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