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Splitting technique and Godunov-type schemes for 2D shallow water equations with variable topography

Dao Huy Cuong|Mai Duc Thanh
대한수학회 (The Korean Mathematical Society)|2024.07|대한수학회보 (Bulletin of the KMS)|제61권 제4호|pp. 969-998|DOI 10.4134/BKMS.b230553

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참고문헌

키워드

accuracyresonantGodunov scheme2D shallow water equationsnonconservativedimensional splitting
주제분류수학

초록

We present numerical schemes to deal with nonconservative terms in the two-dimensional shallow water equations with variable topography. Relying on the dimensional splitting technique, we construct Godunov-type schemes. Such schemes can be categorized into two classes, namely the partly and fully splitting ones, depending on how deeply the scheme employs the splitting method. An upwind scheme technique is employed for the evolution of the velocity component for the partly splitting scheme. These schemes are shown to possess interesting properties: They can preserve the positivity of the water height, and they are well-balanced.

Abstract

We present numerical schemes to deal with nonconservative terms in the two-dimensional shallow water equations with variable topography. Relying on the dimensional splitting technique, we construct Godunov-type schemes. Such schemes can be categorized into two classes, namely the partly and fully splitting ones, depending on how deeply the scheme employs the splitting method. An upwind scheme technique is employed for the evolution of the velocity component for the partly splitting scheme. These schemes are shown to possess interesting properties: They can preserve the positivity of the water height, and they are well-balanced.

참고문헌 (32)

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