This contribution deals with numerical simulations of immiscible two-phase flow in heterogeneous porous media. The hydrodynamic properties of the geological porous media are naturally discontinuous at the Darcy scale, which has to be accounted for by discretization methods. In this talk we focus on handling extreme heterogeneities in the capillary pressure/saturation relation arising, in...
In this work we consider a mixed finite element formulation using the enhanced velocity (EV) method to construct a strongly flux-continuous velocity approximation on spatially non-conforming grids. The EV method was recently generalized to semi-structured grids, in which each subdomain represents its own mesh refinement level of a structured grid with arbitrary inactive cells. The union of...
This work develops the theoretical basis and practical application of a promising class of safeguarding strategy in the context of the solution of implicit timesteps for multiphase multicomponent flows in general.
While classic globalization methods such as the linesearch for sufficient descent are problem independent, they require numerous computationally costly evaluations of the...
Modelling multiphase porous media flows is important in many engineering areas such as geothermal energy extraction, unconfined aquifers, CO2 storage, magma reservoirs and hydrocarbon reservoirs. However, modelling of multiphase porous media flow is very challenging due to various reasons: the relative permeabilities (controlled by the saturation) introduces high non-linearities in the system;...
In reservoir simulation, solving highly nonlinear algebraic equations arising from a fully-implicit discretization is challenging. There is generally no acceptable initial iterate available for multiphase flow and transport problems. Hence, a globalization strategy is usually needed when applying Newton's method to the nonlinear system.
Homotopy continuation, which has been widely adopted...
