Non-oscillatory Spatial Solutions Criterion for Convection-Diffusion Problem

Abstract

The fact that the convection-diffusion problems are essential in nature is supported by the presence of such problems in vast number of applications in both science as well as engineering. Some of these applications involve the computational domain’s grid structure issues in the numerical experiment of fluid dynamics. The paper highlights the important role of convection-diffusion flow parameters in the construction of the grid structure. We propose the a priori criterion formulation to avoid non-oscillatory solutions which is based on both Peclet and grid  numbers, and serves as a systematic approach in setting grid related parameters of interest. Aiming at a more efficient process in choosing grid structure for computational domain, the criterion functions as a standard which also eliminates heuristic process in the scalar concentration prediction. The test cases’ calculated results verify the consistency of the criterion.