A finite volume discretization method for flow on structured and unstructured anisotropic meshes - Merrick, Dane Glen (Department of Mechanical Engineering, 2017)
This project is concerned with advection discretization technology within the field of Computational Fluid Dynamics (CFD). To this end, two novel methods are proposed which are dubbed the Enhanced Taylor (ET) Schemes. The model equation for this work is the advection-diffusion equation with the industrial application being incompressible ow. The objective of the proposed schemes is to achieve increased accuracy on structured and unstructured anisotropic meshes. One of the schemes focuses on improving advection accuracy, and the other on improving total advection-diffusion accuracy. Fundamental to the design of the ET schemes is the primary focus on face accuracy, with the additional incorporation of the up and downwind mesh stretching factors and ow gradients. Additionally, non-linear blending with the existing NVSF scheme was effected in the interest of robustness and stability, particularly on equispaced meshes. The developed schemes, along with prominent linear ĸ-Upwind schemes were critically assessed and compared. Current methods were shown to be at best 3rd and 1st-order accurate at non-equispaced faces and nodes respectively. In contrast, the developed schemes were shown to be up to 4th and 2nd-order accurate. Numerical experiments followed. This involved applying the prominent and developed schemes to solve the 1D advection-diffusion equation on stretched meshes. The 2D case involved incompressible ow in a lid-driven cavity. Anisotropic structured and unstructured meshes were employed. Significant improvements in accuracy were found with the ET schemes, with average reductions in error measuring up to a 50%. In comparison to existing methods, it is proposed that state-of-the-art technology has been developed.