Applications of Finite Difference Methods in Fluid Mechanics

This chapter first discusses the use of stream-vorticity function method and velocity–pressure method to solve two-dimensional incompressible viscous fluid problems. For the stream-vorticity function method, the original N-S equation is replaced by a parabolic vorticity transport equation and an elliptic stream Poisson equation. And for the velocity–pressure method, we mainly introduce the Maker and Cell method (MAC), which is similar to ordinary difference method in the calculation of difference equation. Then in the last part, the difference method dealing with boundary layer problems is introduced.