2D Triangulation and Modeling

This paper presents an advancing reduction technique for 2D quality triangulation in computation domains with complex geometries and its applications to a 2D hybrid FVM model. The advancing reduction technique coarsens a fine initial equilateral triangle mesh (ETM) covering the whole domain by doubling the cell edge length progressively, so that the whole domain can be decomposed into multiple zones with different densities. Each density zone consists of a number of equilateral triangles with different edge lengths; and the density zones are connected to each other with transition layers. The generated triangle meshes are applied to a 2D depth-integrated hydrodynamic model for surface flow simulations, where the unsteady depth-integrated Reynolds equations are solved using a finite volume method (FVM) on a hybrid (triangles and quadrilaterals) unstructured mesh system with collocated variable arrangement. In this model, a new evaluation method for computing the gradients at the cell edges was proposed to improve the solutions affected by the mesh irregularity and non-uniformity. Examples of triangular mesh generation and numerical simulation of hydrodynamic problems will be presented.