ON WELL-POSED BOUNDARY CONDITIONS AND ENERGY STABLE FINITE-VOLUME METHOD FOR THE LINEAR SHALLOW WATER WAVE EQUATION

被引：0

作者：

Prihandoko, Rudi ^{[1
]}

Duru, Kenneth ^{[1
]}

Roberts, Stephen ^{[1
]}

Zoppou, Christopher ^{[1
]}

机构：

[1] Australian Natl Univ, Math Sci Inst, Canberra, ACT 2600, Australia

来源：

ANZIAM JOURNAL | 2024年

关键词：

numerical analysis; finite volume; boundary condition; energy method; shallow water wave equation; SCHEMES;

D O I：

10.1017/S1446181124000191

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite-volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis.

引用

页数：20

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