General Solution for Two-Dimensional Corner Flows Under Darcy's
Yu. A. Semënov, L. J. Cummings · International Journal of Fluid Mechanics Research · 2005
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.