Staggered Grid

Sat, 13 Jun 2026 00:00:00 +0000

In a previous post, the vorticity-streamfunction formulation of the Navier-Stokes equations was used to simulate flow over a backwards facing step. This post will simulate flow over the backwards facing step using the primitive variable approach and a staggered grid.

To briefly summarize, a key advantage of the streamfunction-vorticity approach is that there is no pressure-velocity coupling. This is because there is no pressure term in the vorticity transport equation. However, treatment of boundary conditions is slightly more difficult as values for the streamfunction must also be calculated.

Streamfunction Vorticity

Mon, 08 Jun 2026 23:20:42 -0400

The following post details a code I wrote as part of a CFD course. It simulates flow over a backwards-facing step using the vorticity-streamfunction formulation. Specifically, the assignment was to replicate the results from Roache and Mueller’s 1970 paper “Numerical Solutions of Laminar Separated Flows”.

Vorticity-Streamfunction & Solution Procedure Link to heading

The streamfunction $\psi$ is defined as: $$ u = \frac{\partial \psi}{\partial y}, \quad v = -\frac{\partial \psi}{\partial x} $$

Julia on Jorgen Wu

Staggered Grid

Streamfunction Vorticity

Vorticity-Streamfunction & Solution Procedure Link to heading