On well-posed boundary conditions and energy stable finite volume method for the linear shallow water wave equation

2023/09/28 by Rudi Prihandoko, Prihandoko, Rudi, Kenneth Duru +5
Engineering · Mathematics · #65M08 (Secondary) #65M12 (Primary) #Advanced Mathematical Physics Problems #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2309.16116

openalex publication_date 2023/09/28 · openalex created_date 2023/10/01 · openalex updated_date 2026/07/28

Abstract

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.

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