The Dual Mesh Control Domain Method for Linear and Nonlinear Convection-Diffusion Equations in Two Dimensions
Abstract
In this study, an extension of the Dual Mesh Control Domain Method (DMCDM), formerly known as the Dual Mesh Finite Domain Method [1], introduced to solve Poisson’s equations in 1-D and 2-D domains to convection–diffusion problems including the heat equation and the Navier–Stokes equations governing 2-D flows of viscous incompressible fluids is undertaken. The performance of the DMCDM is compared with those of the popular schemes of the finite volume method (FVM) for various problems common in heat transfer and fluid mechanics. Additionally, the performance of the DMCDM for a 2-D primal mesh of quadratic elements is included. A novel method of satisfying the Scarborough criterion [49] for high Reynolds numbers is also introduced wherein the dual mesh is placed off-center from the primal mesh. The proposal concludes with a discussion of the next steps for the project, including the 2-D quadratic DMCDM for the Navier–Stokes, and a full analysis of the performance of the off-center dual mesh. The method is also expanded into non-rectangular domains with non-orthogonal, unstructured meshes. This was done to provide a wider applicability to a general user of CFD. The method compared well with the FEM and FVM, showing remarkable stability and accuracy on coarse and skewed meshes. An analysis of the performance of the method, as well as a code for future use are provided as well.
Subject
dual-mesh control domain methodfinite volume method
finite element interpolation
convection–diffusion equation
Navier-Stokes equations
numerical schemes
Citation
Martinez, Matthew A. (2022). The Dual Mesh Control Domain Method for Linear and Nonlinear Convection-Diffusion Equations in Two Dimensions. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /198118.