General solution for two-dimensional corner flows under Darcy's law

We consider two-dimensional Darcy flow of a viscous incompressible fluid with a free boundary in a corner between two non-parallel walls. The complex potential of the flow constructed in an auxiliary parameter domain admits a general form for the flow generated by a source/sink at the corner vertex or at infinity, We present a method used to construct the flow potential, and obtain an integral equation for the velocity modulus on the free boundary. We discuss a possible numerical procedure to solve this integral equation, and present sample numerical results concerning the initial shape of the free boundary and its time evolution.