What is it about?

We model and quantify uncertainties in the subsurface flow. Particularly, we solve the density-driven flow problem (Elder problem). We model unknown porosity and permeability coefficients by random fields. As a result, the solution --- the mass fraction is also uncertain. For solution, we adapted the well-known UG4 framework (developed by the group of Prof. Griebel in Frankfurt University). UG4 includes an efficient parallel multigrid algorithm, which is scalable on many hundreds thousands parallel cores. To handle random variables, we construct low-cost generalized polynomial chaos (gPC) expansion. The gPC coefficients are computed by projection. The obtained high-dimensional integrals are computed by sparse grid methods.

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Why is it important?

The obtained results could be useful for agriculture and environmental protection. The considered model describes how fresh drinking water is mixing with the denser salty water.


From the mathematical perspective this problem is not trivial. It is time-dependent and non-linear. The solution process requires fine resolution in time and space. Random perturbations in the porosity may change the stochastic solution, i.e., the number of fingers, their intensity, shape, propagation time and velocity. This problem has also very important practical application.

Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen

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This page is a summary of: Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability, GEM - International Journal on Geomathematics, March 2020, Springer Science + Business Media, DOI: 10.1007/s13137-020-0147-1.
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