## Preprint 2015-13

## Raimund Bürger, Sudarshan K. Kenettinkara, Sarvesh Kumar, Ricardo Ruiz-Baier:

### Finite volume element-discontinuous Galerkin approximation of viscous two-phase flow in heterogeneous porous media

### Abstract:

Runge-Kutta Discontinuous Galerkin (RKDG) and Discontinuous Finite Volume Element (DFVE) methods are applied to a coupled flow-transport problem describing the immiscible displacement of a viscous incompressible fluid in a non-homogeneous porous medium. The model problem consists of a nonlinear pressure-velocity equation assuming Brinkman flow, coupled to a nonlinear hyperbolic equation governing the mass balance (saturation equation). The mass conservation properties inherent to finite volume-based methods motivate a DFVE scheme for the approximation of the Brinkman flow in combination with a RKDG method for the spatio-temporal discretization of the saturation equation. The stability of the scheme for the saturation equation is analyzed. Several numerical experiments illustrate the robustness of the numerical method.

This preprint gave rise to the following definitive publication(s):

**Raimund BüRGER, Sudarshan K. KENETTINKARA, Sarvesh KUMAR, Ricardo RUIZ-BAIER: ***Discontinuous approximation of viscous two-phase flow in heterogeneous porous media*. Journal of Computational Physics, vol. 321, pp. 126-150, (2016).