Instructional Fluid Dynamics in Viscous Flow Part II, Visualization of Flow Patterns Downstream of a Backward Facing Step and Around an Elliptical Cylinder

With the experience of using Tri-Diagonal Matrix Algorithm (TDMA) for solving parabolic partial differential equations (PDE), solutions for elliptic PDEs were obtained by introducing the Alternating Direction Implicit (ADI) scheme. The main objective is to visualize the flow patterns around an aerodynamic body of arbitrary geometry. To understand the basic principle through hand-on experience with minimum resources, the problem assignments were divided into two parts: The first one was to combine the ADI/TDMA method to solve the Navier-Stokes equations for a two-dimensional flow over a backward facing step. The stream function and vorticity approach was developed. The second one was to find the streamline distributions around an elliptical cylinder with zero degree angle of attack. Laplace equations were used to generate a body-fitted-coordinate (BFC) system for relating the physical domain with the computational domain. The Navier-Stokes equations were transformed to the BFC system and solved by the ADI/TDMA method for stream function and vorticity