Proposed Title:

Accurate Finite Volume Methods for the Numerical Simulation of Transport in Heterogeneous Porous Media

The overall aim of this Ph.D project is to develop an accurate finite volume solution technique to solve a representative transport equation for heterogeneous porous media and apply the developed solution technique to some particular industrial case studies. At first, analytical solutions will be derived, considering a rectangular geometry, for some simplified, linear problems. The numerical schemes will be compared directly with these benchmark solutions in order to assess the accuracy and efficiency of the approximations used for the gradient terms, as well as for the entire flux term.

The developed technique then will be extended to the completely non-linear and unstructured mesh case, where the properties of the medium under investigation may vary spatially as a function of the primary solution variable. An example of this situation arises when considering a medium in which the thermal conductivity is a non-linear function of the temperature and the solution domain is of arbitrary shape.