Solution of the Navier–Stokes Equations: Part 1
The additional complexity of the Navier–Stokes equations and special features for incompressible flows are considered in this chapter and the next; here we cover basic issues, the features of the equations, and the methods of solution. The staggered and collocated variable arrangements, the pressure equation, and the pressure-velocity coupling for incompressible flows using the fractional-step and SIMPLE algorithms are described in detail. Other approaches (the PISO algorithm, streamfunction-vorticity, and artificial compressibility) are also briefly described. The initial and boundary conditions for the Navier–Stokes equations and their implementation on Cartesian grids are also covered.