**Numerical Solutions Applied To Heat Transfer And
Fluid
Mechanics Problems**

The SIMPLE Method for solution of the Navier-Stokes Equations

When solving the Navier-Stokes equations for applications in
Computational
Fluid Dynamics (CFD) the most widely used methods have until recently
been based on one developed
by S. V. Patankar and D.B. Spalding named SIMPLE. This class of
method is sometimes referred to as a segregated solver in commercial
CFD packages. See this link
for one description of a problem solution in this family.

Though relatively simple to implement, the SIMPLE iteration strategy
has relatively poor convergence rates. With the advent of
improved linear system solvers such as Krylov and Algebraic
Multigrid, both commercial and home-grown CFD codes are moving to
better iteration strategies with much faster rates of convergence.