CFD Python: the 12 steps to Navier-Stokes equations

Abstract

• Steps 1–4 are in one dimension: (i) linear convection with a step-function initial condition (IC) and appropriate boundary conditions (BC); with the same IC/BCs: (ii) nonlinear convection, and (iii) diffusion only; (iv) Burgers’ equation, with a saw-tooth IC and periodic BCs. • Steps 5–10 are in two dimensions: (v) linear convection with a square function IC and appropriate BCs; with the same IC/BCs: (vi) nonlinear convection, and (vii) diffusion only; (viii) Burgers’ equation; (ix) Laplace equation, with zero IC and both Neumann and Dirichlet BCs; (x) Poisson equation in 2D. • Steps 11–12 solve the Navier–Stokes equation in 2D: (xi) cavity flow; (xii) channel flow.