MPFA and MHFE methods for flow and transport in porous media
Third party funded individual grant
Start date : 01.01.2012
End date : 31.12.2013
Project details
Scientific Abstract
Nonlinear (multiphase) flow and reactive multicomponent transport problems in highly heterogeneous porous media and their numerical simulation are of great interest for evaluating site remediation, energy exploitation or CO2 sequestration scenarios. The resulting advection-diffusion-reaction-systems are coupled nonlinear parabolic partial differential equations, and we have parabolic or elliptic nonlinear flow equations, possibly degenerate. The development of convergent and efficient numerical schemes is very challenging and the mixed (hybrid) finite element method M(H)FEM and the multipoint flux approximation MPFA are powerful locally mass conservative choices. They offer also the advantage of continuous flux approximations over the element faces. Analogies between the two techniques should help to prove order of convergence estimates and monotonicity for the multicomponent transport problems, but also for multiphase flow. Furthermore numerical diffusion of the schemes should be quantified to assess the accuracy of the methods. Simulation examples should include realistic scenarios on heterogeneous, log normally distributed random parameter fields.
