Analysis of different numerical schemes for the resolution of convection- diffusion equations using finite-volume methods on three-dimensional unstructured grids. Part I: Discretization schemes

摘要

This article presents different interrelated numerical criteria for the analysis of both the diffusion and convection terms in convection-diffusion equations: gradient computation, interpolation procedures, diffusion schemes, convective schemes, and boundary conditions. Discretizations are performed on three-dimensional unstructured meshes composed of arbitrary convex polyhedra. A finite-volume cell-centered formulation is used. Most of the numerical criteria are well known in the technical literature, but a number of alternative approaches or variants are also presented. The objective of the article is to analyze these criteria in terms of accuracy, computational effort, and convergence characteristics. A comprehensive numerical study is performed in Part II of this article.