A Simulation Method of 2D Steady Scalar Convection-Diffusion Flow on an Exponentially Graded Mesh

Abstract

Owing to its fundamental nature, convection-diffusion flows are researched in a number of engineering, scientific, and aeronautical applications. The right meshing approaches are necessary for convection-diffusion simulations. Major meshes in computational fluid dynamics that are used to find the solutions to discretized governing equations include uniform, piecewise-uniform, graded, and hybrid meshes. Unintentionally applying the meshes might lead to poor solutions including numerical oscillations, over- or under-predictions, and lengthy computing time. Accentuating the effectiveness of exponentially graded mesh finite-difference scheme, this paper takes the simulation of a 2D steady scalar convection-diffusion into account. The problem was solved by assigning certain mesh expansion factor to the mesh according to Peclet number. The factor was determined based on its previously derived logarithmically linear relationship with low Peclet number. Based on the values of Peclet number and the source, eight groups of test cases are presented in this paper. It was found that given a Peclet and a mesh number, simulation error percentage was surprisingly constant regardless the source values. The rates of convergence for the scheme, however, were comparable with respect to source values. Uniform convergence rate was also found to be achievable in all test cases corresponding to Peclet number of interests. This work successfully assessed the validity range of the generalized logarithmically linear model between exponentially graded mesh expansion factor and Peclet number for the simulation.