Numerical study of two problems in fluid flow: Cavitation and cerebral circulation

Two different computational models of fluid flow are considered. First, the possibility of cavitation is investigated numerically in two and three dimensions for the spherically symmetric, barotropic, Navier-Stokes equations. A splitting method is derived in order to allow the use of known solutions to the corresponding inviscid Euler equations. Results indicate cavitation is possible in the presence of high Mach numbers. This work is intended to be a stepping off point in the search for analytic solutions showing cavitation in multi-dimensional compressible flows.; Second, a blood flow model for circulation in the Circle of Willis (CoW) is derived. It is calibrated using ensemble Kalman filtering and validated against clinical data. The resulting model is then used to predict the effects of common anatomical variations within the CoW on blood perfusion in the brain, both under normal circumstances and in the event of a stroke.