A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary states, different time scales including metastability, as well as concentrations and self-similar behavior induced by singular nonlocal kernels. We use the scheme to explore properties of these equations beyond their present theoretical knowledge

Three-layer approximation of two-layer shallow water equations

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

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples

On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws

Submitted to: SIAM J. Scient. Comput., July 27, (2001). Revised, January 23, (2002)SIGLEAvailable from TIB Hannover: RN 8680(210) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Object-oriented hyperbolic solver on 2D-unstructured meshes applied to the shallow water equations

Fluid dynamics, like other physical sciences, is divided into theoretical and experimental branches. However, computational fluid dynamics (CFD) is third branch of Fluid dynamics, which has aspects of both the previous two branches. CFD is a supplement rather than a replacement to the experiment or theory. It turns a computer into a virtual laboratory, providing insight, foresight, return on investment and cost savings1. This work is a step toward an approach that realise a new and effective way of developing these CFD models.EThOS - Electronic Theses Online ServiceGBUnited Kingdo