Three-layer approximation of two-layer shallow water equations

• Main Authors: Alina Chertock, Alexander Kurganov, Zhuolin Qu, Tong Wu
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2013-12-01
• Series: Mathematical Modelling and Analysis
• Subjects: two-layer shallow water equations; central-upwind scheme; well-balanced scheme; conditional hyperbolicity
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/4145

Two-layer shallow water equations describe flows that consist of two layers of inviscid fluid of different (constant) densities flowing over bottom topography. Unlike the single-layer shallow water system, the two-layer one is only conditionally hyperbolic: the system loses its hyperbolicity because of the momentum exchange terms between the layers and as a result its solutions may develop instabilities. We study a three-layer approximation of the two-layer shallow water equations by introducing an intermediate layer of a small depth. We examine the hyperbolicity range of the three-layer model and demonstrate that while it still may lose hyperbolicity, the three-layer approximation may improve stability properties of the two-layer shallow water system.