Simulation of Flow and Mechanics in the Brain, 2019

Advisors: Florin Radu, Kundan Kumar and Ingeborg Gjerde

Short description of the project:

In this thesis, we study the numerical approximation solving a fully coupled quasi-static, linear Biot model in a 3D domain with 1D line sources. To approximate the problem, we developed a scheme combining two techniques: (i) a splitting technique for solving the pressure and the flux and (ii) the fixed-stress splitting scheme. The scheme here is based on splitting the solution of both the pressure and the flux in the flow equations into one explicitly known, low regularity term, and one implicitly unknown, high regularity term. The flow equations are then solved to get the high regularity terms. In the second step, the theexplicitly-known terms are interpolated onto the discrete space of the pressure and the flux. Thus, obtaining the reconstructed pressure and flux. Finally, to calculate the displacement by solving the mechanics equation with the actual pressure. This scheme has one additional step in comparison to the standard schemes. Optimal convergence was both theoretically and numerically proven for the novel scheme. Lastly, we simulated flow and mechanics for a data set describing a vascular system of a human brain to demonstrate simulations on a dataset with complex geometry.

Link to the thesis at BORA: https://bora.uib.no/bora-xmlui/handle/1956/20035