High order finite element simulations for fluid dynamics validated by experimental data from the FDA benchmark nozzle model

prudhomm Blog, Health, HPC, News, Publication

The objective of the present work is to construct a sound mathematical, numerical and computational framework relevant to blood flow simulations and to assess it through a careful validation against experimental data. We perform simulations of a benchmark proposed by the FDA for fluid flow in an idealized medical device, under different flow regimes. The results are evaluated using metrics proposed in the literature and the findings are in very good agreement with the validation experiment.

Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics

prudhomm Health, Life Sciences, Publication, Research

Pressure driven flows typically occur in hydraulic networks, e.g. oil ducts, water supply, biological flows, microfluidic channels etc. However, Stokes and Navier-Stokes problems are most often studied in a framework where Dirichlet type boundary conditions on the velocity field are imposed, thanks to the simpler settings from the theoretical and numerical points of view. In this work, we propose a novel formulation of the Stokes system with pressure boundary condition, together with no tangential flow, on a part of the boundary in a standard Stokes functional framework using Lagrange multipliers to enforce the latter constraint on velocity. More precisely, we carry out (i) a complete analysis of the formulation from the continuous to discrete level in two and three dimensions (ii) the description of our solution strategy, (iii) a verification of the convergence properties with an analytic solution and finally (iv) three-dimensional simulations of blood ow in the cerebral venous network that are in line with in-vivo measurements and the presentation of some performance metrics with respect to our solution strategy.

Simulation of two-fluid flows using a finite element/level-set method in 3D. Application to two drop benchmarks

prudhomm Blood Rheology, Health, HemoTum++, News, Research

We present a numerical framework for the simulation of three-dimensional multi-fluid flows based on a finite element/level-set approach. The method allows a full Eulerian ” tracking ” of the interfaces between the fluids, and the properties of the interfaces can be directly taken into account as surface forces. The resolution of the fluid equations and the advection of the interface can be easily decoupled, which enables the use of efficient solving strategies. We also present a 3D benchmark of the rise of a drop in a viscous fluid. We use two different setups and compare our results to previous results obtained with other approaches to validate our method.