Dirchilet boundary condition implementation in FVM
I am solving 1D non-linear hyperbolic equation - the Buckley Leverett equation using Finite volume methods.
Here is the equation:Buckley Leverett
I am solving this system using upwinded (for simplicity purposes right now) using fully implicit solver (I have to use fully implicit method due to other reason). I solve it implicitly at each time step using Newton's method - a standard way in reservoir simulation.
I am having some troubles in implementing Dirichlet boundary condition i.e. how to impose a boundary condition on the inlet face in the numerical framework.
1) Should I just add another cell on the left (which is the boundary) of same length "dx" as other cells or should I add a cell of very large length?
2) Further, do I consider this cell - ghost cell as part of my system of equations and solve it?
Thanks in advance for your help.
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