• Research on coupling conditions between the pure liquid flow and the flow in the porous media. These coupling conditions are well studied only in the simple case of parallel flow over a porous media (see the picture below).

Flow in a channel, partially filled with porous media

• Reformulating the problem in the way, that a common system of partial differential equations is governing the flow in the pure liquid and in the plain media. This is done in fictitious regions method manner. The coefficients of the equations in this common system vary in the way, reducing this unique system to Navier-Stokes equations in the liquid zone, and to Brinkmann or Darcy law in the porous media.
• Developing numerical algorithms for the above mentioned system, their software implementation and validation. We adapt some projection methods (like SIMPLE), which are widely used for computing pure liquid incompressible flow, to the needs of computing flow in plain and porous media. The developed algorithm for arbitrary 3D geometry is implemented in C++. Several tests are performed in order to validate the model and the algorithm. One of them concerns 2D flow in a channel, partially filled with porous media. Under certain conditions, this problem can be reduced to a 1D problem, which can be solved analytically. The following picture presents comparison of 2D numerical solution with the analytical solution of the 1D model problem (green line).

Comparison of numerical and analytical solutions for a model problem

• Investigating real problems. Numerical simulation of oil flow within a filter box gives detailed information about the velocity and pressure distribution and thus assist the design of more efficient filters. In this case one has to account for flow in two pure liquid regions, separated by the porous filter. The upper part of a filter box is shown below, followed by a figure, representing distribution of the mass flux from the upper surface of the filter. Highly nonuniform loading of the filter can be observed there. Varying the geometry of the filter box, a better performance of the filter can be achieved.

Upper part of a filter box

Flux distribution along the filter