Abstract

This is the second part of a series of lectures on the projection method for viscous incompressible flows. The underlying idea of projection method for solving viscous incompressible flow problems was first introduced independently by Chorin and Temam around 1968. This approach is based on applying the Helmholtz-Hodge decomposition to the incompressible Navier-Stokes equations. The most attractive feature of projection method is that one only needs to solve a sequence of decoupled elliptic equations for the velocity and the pressure at each time step. Therefore, it is very efficient for large-scale numerical simulations. In this talk, we will give a brief review of two variants of the projection method, namely the velocity-correction scheme and the consistent splitting scheme.

Reference:

J. L. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, 195 (2006), pp. 6011-6045.