This is a project for someone who enjoys programming as much as mathematics. Flow through filters, soils and underground rock happens in a maze of pores far too fine to simulate everywhere. Multiscale methods replace the maze by a simpler averaged equation, whose coefficients come from small simulations on a single repeating piece of the material. The ideas are classical. Turning them into a solver that is fast, reliable and trusted is not. You will develop homogenisationFoam, our extension of OpenFOAM, the open-source C++ finite-volume library used widely in industry and research. That means implementing and verifying numerical schemes, running large simulations in parallel, comparing the averaged model with full pore-by-pore computations, and finding out when the cheap model can be trusted. Good software practice is part of the job: version control, automated tests, documentation. There is potential to collaborate with SLB on subsurface applications such as geothermal energy, and you will finish with a code other people use.
Matteo Icardi
Multiscale Modelling and Heterogeneous Media
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