Finite-Point Simulation of Steady Shallow Water Flows

Abstract

Finite-point (FP) methods are novel meshless numerical approaches for solving partial differential equations. Only the nodal data and a description of the domain boundary geometry are necessary. As no element or grid connectivity is needed, mesh-related problems are avoided. This advantage is particularly useful when solving shallow water equations for complicated domains with irregular topography and variable bed roughness. This paper presents an FP model of the element-free Galerkin-type for simulating 2D steady shallow river flows. An attempt is also made to give a state-of-the-art overview of FP methods. The advantages of FP methods are summarized, and their applicability for simulating shallow water flows are discussed.