[Kappa]

Hello everybody,

I know there is much literature and already asked questions concerning this question, but I do not get into this topic:

What is the difference between the PISO and the SIMPLE algorithm?

I know the following:

• In the momentum equation there is a nonlinear part (e.g. u*u for the x-component).
• In the momentum equation there are two unknowns: velocity and pressure. Thus, they are coupled with each other.

Okay, as I understood the PISO algorithm aims at correctly coupling pressure and velocity, since this is very important for transient flows. Since one uses small time steps the nonlinearity u(new)*u(new) can be replaced by the linear term u(old)*u(new).
The SIMPLE algorithm uses large time steps so as to get quickly to a steady-state. Thus, it concentrates on the non-linearity.
PIMPLE just does both and is kind of mergend SIMPLE-PISO.

The questions remaining for me are:

1. SIMPLE also produces a solution where pressure and velocity field are consistent, doesn't it? But how does it achieve that if it does not look on the coupling?
2. Which qualitative effect has the usage of PISO and not considering the non-linearity om the solution?
3. Somewhere it said that PIMPLE is even faster than PISO, so why should I use PISO?
4. Why does SIMPLE need an under-relaxation of the pressure?

Thanks everybody for help. I know this is kind of an easy question but some month ago, I implemented SIMPLE by myself and I think it was not the same as OpenFOAM uses, so I'm kind of confused.

[Coris]

I just came across this book: https://www.researchgate.net/publica..._and_OpenFOAMR

It is a book titled "Mathematics, Numerics, Derivations and OpenFOAMR" by Tobias Holzmann. Chapter 10 is on simple, piso and pimple and the practical application of it. It should solve some of your questions.