Comparative Study of Uniform and Graded Meshes for Solving Convection-Diffusion Equation with Quadratic Source

Abstract

Due to its fundamental nature, the problems of convection-diffusion are discussed in various aviation, science and engineering applications. Among major applications are in the study of the dynamics of aircraft wake vortex and its interaction with turbulent jet which is a very serious hazard in aviation. Other applications include those in the investigation of intrusive sampling of jet engine exhaust gases, and the effectiveness of hot fluid injection in the removal of ice on aircraft wings. The numerical solutions of convection-diffusion require proper meshing schemes. Among major meshes in computational fluid dynamics are those of uniform, piecewise-uniform, graded, and hybrid over which the solutions of discretized governing equations are found. Bad solutions as spurious fluctuations, over- or under-predictions, and excessive computation time might be the results of unwitting application of the meshes. Accentuating comparative effectiveness of two meshes, namely uniform mesh and graded mesh with mesh expansion factor, this paper takes the solution of a convection-diffusion equation with quadratic source term into account. The problem is solved by assigning several values of mesh expansion factor to graded mesh, while mesh number is kept constant. The factors are calculated based on the generalization of their logarithmically linear relationship with low Peclet numbers derived in previous work. Based on the values of Peclet number, five test cases are considered. Graded mesh is proven relatively more robust, particularly due the solution on the mesh being free from spurious fluctuation. Furthermore, the accuracy level of the solution of up to two order of magnitude higher is obtained. The mesh expansion factor therefore contributes to a stable and highly accurate solution corresponding to all interested Peclet numbers.