In this condition, by taking the divergence of all terms in the momentum equation, one obtains the pressure poisson equation. For an incompressible flow this constraint is given by: where is the velocity in the direction, is velocity in and is the velocity in the direction. Taking divergence of the momentum equation and using the incompressibility constraint, the pressure Poisson equation is formed given by: where is the kinematic viscosity of the fluid and is the velocity vector. The discrete Poisson's equation arises in the theory of Markov chains. It appears as the relative value function for the dynamic programming equation in a Markov decision process, and as the control variate for application in simulation variance reduction. Footnotes References Hoffman, Joe D., Numerical Methods for Engineers and Scientists, 4th Ed., McGraw–Hill Inc., New York, 1992. Sweet, Roland A., SIAM Journal on Numerical Analysis, Vol. 11, No. 3 , June 1974, 506–520. Finite differences Numerical differential equations