Solution of Poisson's equation
In CFD the Poisson equation occurs mainly in the form:
The left hand side can be discretised in the manner explained in section related to diffusive term . The diffusive term can be broken into two explicit and implicit parts.
giving us the expression:
where and are suitable face averages.
When broken into implicit and explicit parts
This gives us the coefficient of matrix as:
and for source matrix:
Once the coefficient and source matrix is constructed, the system could be solved with the help of iterative solvers.