Discrete Poisson equation: Difference between revisions

m (Undid revision 495441442 by Kri (talk) One equation can describe many equations if it is in matrix form)
(→‎Applications: clarify)
== Applications ==
 
In [[computational fluid dynamics]], for the solution of an incompressible flow problem, the incompressibility condition acts as a constraint for the pressure. There is no explicit form available for pressure in this case due to a strong coupling of the velocity and pressure fields. 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:
 
For an incompressible flow this constraint is given by:
:<math>
\frac{ \partial v_x }{ \partial x} + \frac{ \partial v_y }{ \partial y} + \frac{\partial v_z}{\partial z} = 0
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