A validation study of a software implementation of the Gauge method for the incompressible Navier-stokes equations

The incompressible Navier-Stokes equations model the relationship between the velocity and pressure of a fluid and can be used to describe the motion of a fluid. Because they are nonlinear, they are in most cases difficult or impossible to solve analytically. They must, therefore, be approximated numerically. One approach developed by Alexandre Chorin is to use a projection method to approximate the pressure and velocity. We will look at Chorin’s approach and then consider a modified approach called the gauge method, which mitigates some of the boundary condition difficulties in Chorin’s approach. We will then consider an improvement to the gauge method that gives us second order convergence in the velocity in both time and space and slightly better than order 3/2 convergence in the pressure in time. We will then present a code to automate the gauge method and consider some test cases to verify that the code converges at the appropriate rate.