A meshless solution of two dimensional multiphase flow in porous media

Multiphase fluid flow problems are of importance in many disciplines including hydrology and petroleum reservoir engineering. Standard methods such as the finite differences, finite volumes and expanded mixed finite elements methods use very general unstructured grids and need different grid adaptation strategies to ensure optimal solution of this non-linear problem. The meshless methods seem to be quite a good alternative to these classical mesh-based methods. In our work we used the meshless Petrov–Galerkin local method based on the pressure-saturation formulation.