[velkon]

In some papers I find that it is important for a turbulence model to meet the solvability conditions, like in [Pomraning, E., "Development of Large Eddy Simulation Turbulence Models," Ph.D. Thesis, University of Wisconsin-Madison, Madison, WI, 2000.] for the dynamic structure section.

In https://imechanica.org/files/CFD.pdf I found regarding the solvability conditions that: If these conditions are met, the solution of the pressure-Poisson equation and momentum equation is equivalent to the solution of the momentum equation along with a divergence constraint.

However, I still do not understand what this actually means. Could someone provide a more understandable explanation of the solvability conditions?

[FMDenaro]

Originally Posted by velkon

In some papers I find that it is important for a turbulence model to meet the solvability conditions, like in [Pomraning, E., "Development of Large Eddy Simulation Turbulence Models," Ph.D. Thesis, University of Wisconsin-Madison, Madison, WI, 2000.] for the dynamic structure section.

In https://imechanica.org/files/CFD.pdf I found regarding the solvability conditions that: If these conditions are met, the solution of the pressure-Poisson equation and momentum equation is equivalent to the solution of the momentum equation along with a divergence constraint.

However, I still do not understand what this actually means. Could someone provide a more understandable explanation of the solvability conditions?

That has nothing to do with turbulence models. It is the condition that allows us to solve the pressure equation with Neumann BCs while considering that the matrix of the system is singular. The compatibility relation is a supplementary condition that allow to get a non-unique solution for the pressure. This relation is the one you get from the Poissone problem (question + BCs) in integral form and considering the continuity constraint.