A computational method for solving the branched channel flow problem

In the present work, a method is suggested to find the solution of Poisson's equation with Dirichlet boundary conditions in polar coordinates. This method is expressed over the unit circle and consequently over the upper-half plane from which geometry we find the solution to Poisson's equation over the branched channel domain. The results seems very reasonable and the derived transformation from unit circle to Y-shape channel is accurate. Poisson's equation can be solved similarly over much other geometry. The solution looks very encouraging and resembles that is experimentally known.