Channel Flow Solver in Vorticity Streamfunction Formulation

A solver for the 2D channel flow problem in vorticity streamfunction formulation of the Navier-Stokes-Equations

This code solves the 2D-channel-flow problem (steady, incompressible) in vorticity-streamfunction formulation using finite difference approximations. After computing initial values for the vorticity field, the iteration starts with solving for the streamfunction using the Jacobi Iteraition. Subseuqently, the vorticity on the boundary is found and the transport equation solved by an upwind scheme to counter numerical diffusion. Finally, U and V velocities are extracted from the streamfunction.

NOTE: As we are looking for the steady state solution, a single computation of the Jacobi Iteration is enough. The computation of residuals is only necessary for unsteady computations.

Reference: Salih, A. (2013, March). Streamfunction-Vorticity Formulation. Indian Institute of Space Science and Technology, Department of Aerospace Engineering. Retrieved May 11, 2020, from https://www.iist.ac.in/sites/default/files/people/psi-omega.pdf