2D unstructured mesh generation for oceanic and coastal tidal models from a localized truncation error analysis with complex derivatives

A method for computing target element size for tidal, shallow water flow is developed and demonstrated. The method, Localized truncation error analysis with complex derivatives (LTEA-CD) utilizes localized truncation error estimates of the linearized shallow water momentum equations consisting of complex derivative terms. This application of complex derivatives is the chief way in which the method differs from a similar existing method, LTEA. It is shown that LTEA-CD produces results that are essentially equivalent to those of LTEA (which in turn has been demonstrated to be capable of producing practicable target element sizes) with reduced computational cost. Moreover, LTEA-CD is capable of computing truncation error and corresponding target element sizes at locations up to and including the boundary, whereas LTEA can be applied only on the interior of the model domain. We demonstrate the convergence of solutions over meshes generated with LTEA-CD using an idealized representation of the western North Atlantic Ocean, Caribbean Sea and Gulf of Mexico.     

Two‐dimensional,unstructured mesh generation for tidal models

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.     

Automatic,unstructured mesh generation for tidal calculations in a large domain

An automated procedure is described for the production of unstructured, finite element meshes to perform depth-integrated, hydrodynamic calculations in an ocean-scale, two-dimensional domain. Three relatively coarse meshes with nearly identical boundaries are automatically produced by basing internal size guidelines on a localized truncation error analysis that was performed using results from a highly resolved mesh.

Qualitative and quantitative comparisons of model performance are made at 150 historical tidal stations. The coarsest mesh is shown to meet or exceed the overall accuracy of the other meshes, including a highly resolved mesh that has over six times as many computational points. The automated procedure quickly and easily produces a computationally efficient and accurate finite element mesh that is reproducible. In addition, the methodology is shown to have potential for assessing the importance and accuracy of and bathymetric details and evaluating historical hydrodynamic data.