Graded Mesh Number Effect on the Solution of Convection-Diffusion Flow Problem with Quarter-Circle Source

Convection-diffusion equations are fundamental to modeling various transport phenomena in engineering and scientific applications. However, solving these equations accurately poses significant numerical challenges, particularly under conditions involving sharp gradients or weak singularities. This study investigates the influence of graded mesh intervals on the numerical accuracy of a two-dimensional convection-diffusion flow problem featuring a quarter-circle source. The research focuses on low Peclet number regimes where diffusion dominates and solution precision is highly sensitive to mesh configuration. The study utilizes a logarithmic model to generate graded mesh intervals governed by an expansion factor. Sixteen test cases are developed by applying various mesh spacings to selected Peclet numbers. The numerical solutions are analyzed to quantify error reduction and assess the convergence behavior across different mesh densities. The results demonstrate a clear relationship between mesh refinement and solution accuracy, highlighting the graded mesh’s ability to suppress numerical artifacts such as spurious oscillations and excessive diffusion or dispersion errors. Findings show that the use of graded meshes significantly enhances the accuracy of scalar concentration profiles, validating their effectiveness in handling convection-diffusion problems with geometric complexities like quarter-circle sources. Additionally, the computed orders of accuracy confirm the robustness of the meshing technique, offering practical insights for optimizing computational resources while maintaining reliability. The study concludes that selecting appropriate graded mesh parameters—specifically tailored through a logarithmic model—can serve as a heuristic guide for achieving predictable numerical accuracy in convection-diffusion simulations. This work contributes to the broader understanding of meshing strategies in computational fluid dynamics, particularly for low Peclet number applications. It also supports the development of more efficient and accurate solvers for problems characterized by mixed convective and diffusive transport, such as the convection-diffusion of water vapor used to describe the dynamics of aircraft wake vortices.