In this work, we present a numerical scheme for the approximate solutions of a 2D crawling cell migration problem. The model, defined on a non-deformable discoidal domain, consists in a Darcy fluid problem coupled with a Poisson problem and a reaction-advection-diffusion problem. Moreover, the advection velocity depends on boundary values, making the problem nonlinear and non local. \par For a discoidal domain, numerical solutions can be obtained using the finite volume method on the polar formulation of the model. Simulations show that different migration behaviours can be captured.