High-order finite-element framework for the efficient simulation of multifluid flows

International audienceWe present in this paper a comprehensive framework for the simulationof multifluid flows based on the implicit level-set representation of interfacesand on an efficient solving strategy of the Navier-Stokes equations. Themathematical framework relies on a modular coupling approach between thelevel-set advection and the fluid equations. The space discretization isperformed with possibly high-order stable finite elements while the timediscretization features implicit Backward Differentation Formulae of arbitraryorder. This framework has been implemented within the Feel++ library,and features seamless distributed parallelism with fast assembly procedures forthe algebraic systems and efficient preconditioning strategies for theirresolution. We also present simulation results for a three-dimensional multifluidbenchmark, and highlight the importance of using high-order finite elements forthe level-set discretization for problems involving the geometry of theinterfaces, such as the curvature or its derivatives

Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles

In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore flow in both two and three dimensions. These algorithms rely on alternating diffusions of the signed distance function to the interface and a redistanciation step, and with careful choice of the applied diffusions, end up moving the zero level-set of the distance function by some geometrical quantity without resorting to any explicit transport equation. The constraints are enforced between the diffusion and redistanciation steps via a simple rescaling method. The energy globally decreases at the end of each global step. The algorithms feature the computational efficiency of thresholding methods without requiring any adaptive remeshing thanks to the use of a signed distance function to describe the interface. This opens their application to dynamic fluid-structure simulations for large and realistic cases. The methodology is validated by computing the equilibrium shapes of two- and three-dimensional vesicles, as well as the Clifford torus

feelpp/feelpp: v0.103.2

:gem: Feel++: Finite Element Embedded Language and Library in C+

Hemodynamic forces tune the arrest, adhesion and extravasation of circulating tumor cells

International audienc

Hemodynamic forces tune the arrest, adhesion and extravasation of circulating tumor cells

International audienc