Explicit Lid Driven Cavity Solution with Third-Order Upwinding Term, Python

Converted a multi-grid FD matrix solution from MATLAB to python. All terms of the Navier-Stokes equation are handled explicitly, with the convective operator using B.P. Leonards bi-directional Third Order Upwinding and the laplacian being centered difference.

Dump frequency was set to 300 iterations. Time step was variable, depending on the maximum component velocity and the grid size. A 129x129 grid was used to compare to Ghia et al. JOURNAL
OF COMPUTATIONAL PHYSICS 48, 387-411 (1982) reference data. Ghia uses a stream function and vorticity transport equation to solve for the Navier-Stokes. Slight differences arise in this work versus Ghia et al. at Re=100 possibly explained by the explicit scheme versus implicit. Fluid behaviour does appear to follow Ghia et al., but not to the same magnitudes.

Python