Two‐dimensional, unstructured mesh generation for tidal models

Abstract

The successful implementation of a finite element model for computing shallow-water flow requires the identification and spatial discretization of a surface water region. Since no robust criterion or node spacing routine exists, which incorporates physical characteristics and subsequent responses into the mesh generation process, modelers are left to rely on crude gridding criteria as well as their knowledge of particular domains and their intuition. Two separate methods to generate a finite element mesh are compared for the Gulf of Mexico. A wavelength-based criterion and an alternative approach, which employs a localized truncation error analysis (LTEA), are presented. Both meshes have roughly the same number of nodes, although the distribution of these nodes is very different. Two-dimensional depth-averaged simulations of flow using a linearized form of the generalized wave continuity equation and momentum equations are performed with the LTEA-based mesh and the wavelength-to-gridsize ratio mesh. All simulations are forced with a single tidal constituent, M2. Use of the LTEA-based procedure is shown to produce a superior (i.e., less error) two-dimensional grid because the physics of shallow-water flow, as represented by discrete equations, are incorporated into the mesh generation process. Copyright © 2001 John Wiley & Sons, Ltd.