  Mechanical models for tumor growth have been used extensively in recent years
for the analysis of medical observations and for the prediction of cancer
evolution based on imaging analysis. This work deals with the numerical
approximation of a mechanical model for tumor growth and the analysis of its
dynamics. The system under investigation is given by a multi-phase flow model:
The densities of the different cells are governed by a transport equation for
the evolution of tumor cells, whereas the velocity field is given by a Brinkman
regularization of the classical Darcy's law. An efficient finite difference
scheme is proposed and shown to converge to a weak solution of the system. Our
approach relies on convergence and compactness arguments in the spirit of Lions
(Mathematical Topics in Fluid Dynamics, 1998).
