@article{devault_gremaud_novak_olufsen_vernieres_zhao_2008, title={BLOOD FLOW IN THE CIRCLE OF WILLIS: MODELING AND CALIBRATION}, volume={7}, ISSN={["1540-3467"]}, DOI={10.1137/07070231X}, abstractNote={A numerical model based on one-dimensional balance laws and ad hoc zero-dimensional boundary conditions is tested against experimental data. The study concentrates on the circle of Willis, a vital subnetwork of the cerebral vasculature. The main goal is to obtain efficient and reliable numerical tools with predictive capabilities. The flow is assumed to obey the Navier-Stokes equations, while the mechanical reactions of the arterial walls follow a viscoelastic model. Like many previous studies, a dimension reduction is performed through averaging. Unlike most previous work, the resulting model is both calibrated and validated against in vivo data, more precisely transcranial Doppler data of cerebral blood velocity. The network considered has three inflow vessels and six outflow vessels. Inflow conditions come from the data, while outflow conditions are modeled. Parameters in the outflow conditions are calibrated using a subset of the data through ensemble Kalman filtering techniques. The rest of the data is used for validation. The results demonstrate the viability of the proposed approach.}, number={2}, journal={MULTISCALE MODELING & SIMULATION}, author={Devault, Kristen and Gremaud, Pierre A. and Novak, Vera and Olufsen, Mette S. and Vernieres, Guillaume and Zhao, Peng}, year={2008}, pages={888–909} }
 @article{devault_gremaud_jenssen_2007, title={Numerical investigation of cavitation in multidimensional compressible flows}, volume={67}, ISSN={["1095-712X"]}, DOI={10.1137/060652713}, abstractNote={The compressible Navier–Stokes equations for an ideal polytropic gas are considered in ${R}^n$, $n = 2,3$. The question of possible vacuum formation, an open theoretical problem, is investigated numerically using highly accurate computational methods. The flow is assumed to be symmetric about the origin with a purely radial velocity field. The numerical results indicate that there are weak solutions to the Navier–Stokes system in two and three space dimensions, which display formation of vacuum when the initial data are discontinuous and sufficiently large. The initial density is constant, while the initial velocity field is symmetric, points radially away from the origin, and belongs to $H^s_{loc}$ for all $s < n/2$. In addition, in the one-dimensional case, the numerical solutions are in agreement with known theoretical results.}, number={6}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Devault, Kristen J. and Gremaud, Pierre A. and Jenssen, Helge Kristian}, year={2007}, pages={1675–1692} }