期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 14, 页码 5587-5609出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.03.042
关键词
Shallow water equations; Energy preserving schemes; Energy stable schemes; Eddy viscosity; Numerical diffusion
资金
- ONR [N00014-09-10385]
- NSF [DMS10-08397]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1008397] Funding Source: National Science Foundation
We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one and two space dimensions, and (ii) one-dimensional moving equilibrium states. Suitable energy stable numerical diffusion operators, based on energy and equilibrium variables, are designed to preserve these two types of steady states. Several numerical experiments illustrating the robustness of the energy preserving and energy stable well-balanced schemes are presented. (C) 2011 Elsevier Inc. All rights reserved.
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