Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)We present numerical approaches for solving a pseudo-parabolic partial differential equation, which models incompressible two phase flow in porous media taking into account dynamic effects in the capillary pressure. First, we briefly discuss two numerical schemes based on the operator splitting technique. Our numerical experiments show that the standard splitting, widely used to solve parabolic problems, may fail when applied to pseudo-parabolic models. As an illustration, we give an example for this case. So we present an operator splitting scheme based on a dispersive-like character that obtains correct numerical solutions. Then, we discuss an unsplit efficient numerical modelling, locally conservative by construction. This framework is based on a fully coupled space time mixed hybrid finite element/volume discretization approach in order to account for the delicate local nonlinear balance between the numerical approximations of the hyperbolic flux and the pseudo-parabolic term, but linked to a natural dispersive like character of the full pseudo-parabolic equation. We compare our numerical results with approximate solutions constructed with methods recently introduced in the specialized literature, in order to establish that we are computing the expected qualitative behaviour of the solutions. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.1372948FAPESP [2014/03204-9, 2011/23628-0]CNPq [445758/2014-7]IMECC/UNICAMP CAPES-PROEX [23038.004811/2015-42]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)6th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN)JUN 01-05, 2015Pau, FRANCE