Elliptic Grid Generation around NACA0012 Airfoil Based on Algebraic Transformation, Laplace, and Poisson Equation

This project presents a platform of how to create an efficientgrid over an airfoil by comparing different grid generationtechniques. Here two grid generation methods such asalgebraic grid generation method and elliptic grid generationmethod were chosen.The algebraic equation is used to relatethe grid point in the computational domain to those of thephysical domain. This is achieved by using hyperbolictangent scheme between the specified boundary grid pointsto generate the interior grid points. The second methodhighlights the solution for a system of elliptic equations inthe form of Laplace’s and Poisson’s equations in thephysical domain with the help of Point Successive overRelaxation (PSOR) method. These two methods reveal theprocess of generating as well as communicate benefits drawbacks to both algebraic and elliptic methods. In the course ofgrid generation, the magnitudes of the required controlfunctions might be very large in a region where clusteringgrids are needed. On the other hand, there are subtledifferences between the algebraic grid and elliptic generatorone without control function. Based on this, implementationof the Vincour function has no effect on the orthogonality ofgrid system, while it makes the same system more clustered.We will also demonstrate that solving of the Poissonequation will result in a more coherent grid, based onorthogonality and clustering of the grid system.

کلیدواژه ها:

Elliptic O-type Grid Generation ، Hyperbolic Tangent Scheme ، Control Functions ، Vincour Function