I'm trying to write a program based on SIMPLE algorithm (in 1D situation) using book by S.V. Patankar "Numerical Heat Transfer and Fluid Flow". And I have a question related to Section 6.4 In the whole procedure (section 6.7-1, page 126) in point 2 is said to calculate velocity field u* using guessed pressure field p* and eq. 6.8 (also 6.9 in 2D and 6.9&6.10 in 3D). How can I calculate coefficients anb in those equations? As I understand, the right equations for them are 5.57 page 99&100, but they are function of velocity which I don't know. Should I solve set of this equaions by iteration guessing velocity field at the beginning? And where should I calculate this coefficient anb? On faces of staggered grid crossing main grid points? Or or on faces of main grid cells?

Can anyone help me?

This is right, The coefficients anb contain the unknown velocities (or massfluxes). You can start your (iterative) calculation with a guessed velocity field, calculate the massfluxes and build the anbs. Then (in SIMPLE) you solve the momentum equations. After this you build the coefficients of the pressure correction equation. The right hand side of the pressure correction contains the divergenz of the mass, so you build new massfluxes with the new velocities from the momentum solution! After solving the pressure correction you correct pressure, velocities and massfluxes. You can start now the next iteration (outer iteration) and build the momentum coefficients with the corrected massfluxes from the pressure correction equation. You do outer iteration until your convergence criterion is fullfilled.

I can recommend to read the book "Computational Fluid Dynamics" by Ferziger and Peric, there the whole discretization procedure and the SIMPLE Algorithm ist described very well!

Good Luck, Michael!

Thanks a lot. I suspected that guessing velocity field is needful, but this is not mentioned in section 6.7-1 where the whole algorithm is sumarized, and that's why I was confused. It is only said to guess the pressure field p*.

But in case of guessing a velocity and pressure field at the beginning, may those two fields be irrespectieve of each others, or should they be dependent, and somehow linked, for example via dynamic pressure, pd=0.5*density*velocity^2 ?

And another question that comes to me is connected with coefficient b (eq. 6.23h page 125) in p' equation (eg. 6.21). This coefficient is so called "mass source" which this equation should annihilate. In this coefficient appears density at time t+Dt. How to calculate it? May I use corrected pressure valuses gained from iteration and calculate it as Density = Density0*Pressure/Pressure0 ?