Hi everybody, I want to use a relaxation method to resolve the PPE. But the source term of the Poisson equation is discontinuous.

Is it a problem for this kind of iterative resolution?

You can use SOR and minimize the residual... I don't know if it is still actually a projection but it works. See

WELCH, J. E., HARLOW, F. H., SHANNON, J. P., and DALY, B. J., "THE MAC METHOD a computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surfaces," Report LA-3425, Los Alamos Scientific Laboratory, 1965.

or

HARLOW, F. H. and WELCH, J. E., "Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface," Physics of Fluids, vol. 8, pp. 2182â€"2189, Dec. 1965.

Hello Dear Mr Davoche in Pressure poisson equation method in non-staggered grid, two problem occure.1) satisfaction of continuity equation 2) satisfaction of compatibility condition. if you have any paper about compatibility condition Please kindly send me. thank you. best wishes Behzad

Hello Behzad, What do you mean by compatibility condition ?

thank you for the mail. but about your issue: any discretized numerical molecule must to satisfy comtibility condition on calculational domain. compatibility condition is derived from Green theorm(or guse-divergence theorm). unsatisfaction of compatibility condition on non-staggered grid relates to the source term of pressure poisson equation and Numman pressure boundary condition. for more details you can refer to the roach's book. your faitfully Behzad

Hi, I've search for compatibilty condition in Roache' book, and all is right for me.

I have a zero integrale for the Source term and my Neumann condition is a zero gradient on boundary...

So, I don't underdstand why it doesn't converge...