Abstract: Computer powers are often not sufficient to model highly complex finescale processes on large scales.
Our aim is therefore to develop "upscaling" techniques to allow a simulation of simpler physical processes including subgrid terms which account for the more complex finescale processes.
We want to consider two different directions, as you can see in the figure: first, we will concentrate on the upscaling of heterogeneous formations to study the processes and implement
the problem structure and second, we will deal with the upscaling of complex processes such as twophase  twocomponent processes for a twophase simulation in homogeneous media.
The final goal is to unify the two directions to consider the upscaling of complex processes in heterogeneous media.
Further extensions of this model concept are possible.
Especially, we could consider complex finescale processes other than the treated twophase  twocomponent processes, such as isothermal  nonisothermal systems.
Numerical Aspects
We want to use a higher order discontinuous Galerkin (DG) method for an IMPES (implicit pressure  explicit saturation) formulation of twophase flow,
respectively an IMPESC (implicit pressure  explicit saturation and concentration) formulation of twophase  twocomponent flow.
For the solution of the pressure equation, fast multigrid methods exist.
The solution of the saturation equation will be performed using the DG space discretization with higher order explicit RungeKutta schemes for the time discretization.
The advantages of the DG method are not only a fast solution with low numerical dispersion which is an especially crucial point for the simulation on coarse meshes, but also local mass conservativity,
flexible mesh handling and applicability to elliptic, parabolic, and hyperbolic problems.
Oscillations due to the higher order schemes will be overcome using slope limiters.
Part I: Upscaling of Heterogeneous Formations
To achieve our first goal concerning the upscaling of twophase flow in heterogeneous media, we will take the following steps.
First, we will consider a linear twophase problem, without gravity, capillary effects, sources, and with constant phase densities. In the second step, we will extend it to a nonlinear problem.
Next, we will include capillarity and in the last step, we will extend our model to the compressible case.
Concerning the upscaling of these equations, approaches for the first two steps exist for the linear case and for the nonlinear case.
For the other two steps, approaches still have to be developped.
Part II: Upscaling of complex finescale processes
To achieve our second goal, we want to develop an upscaling technique based on the IMPESC formulation of the twophase  twocomponent model problem.
We will first develop a model concept allowing the description of twocomponent processes in a twophase framework and then implement it into the upscaling framework prepared in part I.
