I'm trying to make a CFD model where I can place a source and a sink anywhere in a grid and get the fluid flow rate across each cell boundary between those locations. I'm starting simple with a 3x3 grid and solving continuity for each grid element, but that leaves me a few equations short (9 equations, 12 unknowns). In general I'd like to be able to raise that to a 64x64 grid with multiple flow inputs.
Is there a way to constrain the system such that I can solve it with continuity equations or is this more difficult than I had initially thought?
Below is a simple diagram of my 3x3 grid (o = source, x = drain):
------- |o| | | ------- | | | | ------- | | |x| -------
within the above grid is 9 cells and 12 cell boundaries. How do I fully constrain the system to solve for the flow?
edit: doing some reading on CFD, it would seem that storing the velocity for the CENTRE of each cell is advantageous and the boundary velocities would be calculated based on the centre values for surrounding cells... Although I still don't entirely know how my equations would look with that.