A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocity and continuous capillary pressure
نویسندگان
چکیده
We consider the slightly compressible, two-phase flow problem in a porous medium with capillary pressure. The problem is solved using the implicit pressure, explicit saturation method (IMPES), and the convergence is accelerated with iterative coupling of the equations. We use discontinuous Galerkin to discretize both the pressure and saturation equations. We apply two improvements, which are projecting the flux to the mass conservative H(div)-space and penalizing the jump in capillary pressure in the saturation equation. We also discuss the need and use of slope limiters, and the choice of primary variables in discretization. The methods are verified with two and three dimensional numerical examples. The results show that the modifications stabilize the method and improve the solution.
منابع مشابه
A Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media
In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...
متن کاملOn the solution of incompressible two-phase ow by a p-version discontinuous Galerkin method
where u = − K∇p is the Darcy phase velocity, proportional to the gradient of the phase pressure p . The other coe cients in the model are: the porosity, q a source term, the phase mobility and K the permeability of the porous medium. The di erence between the phase pressures is the capillary pressure pc =pn − pw and we also assume that the sum of the phase saturations is equal to one. The bound...
متن کاملA fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential / capillary potential formulation of the twophase flow system. After discretizing ...
متن کاملDiscontinous Galerkin and Mixed-Hybrid Finite Element Approach to Two-Phase Flow in Heterogeneous Porous Media with Different Capillary Pressures
A modern numerical scheme for simulation of flow of two immiscible and incompressible phases in inhomogeneous porous media is proposed. The method is based on a combination of the mixed-hybrid finite element (MHFE) and discontinuous Galerkin (DG) methods. The combined approach allows for accurate approximation of the flux at the boundary between neighboring finite elements, especially in hetero...
متن کاملNumerical simulation of two-phase immiscible incompressible flows in heterogeneous porous media with capillary barriers
We present a new version of the sequential discontinuous Galerkin method introduced in [25] for two-phase immiscible incompressible flows in heterogeneous porous media with a discontinuous capillary field. Here, a new implementation of the extended interface condition, that does not use the threshold saturation value at the interface and permits treatment of different residual saturations in di...
متن کامل