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A stable scheme for simulation of incompressible flows in time-dependent domains and hemodynamic applications

Banff International Research Station for Mathematical Innovation and Discovery

We present a stable finite-element scheme for incompressible flows in time-dependent domains. The time step is independent of the mesh size, and only one linear system is solved on each time step. We consider fluid-structure interaction (FSI) and Navier-Stokes equations in time-dependent domains. The properties of the scheme are shown on several benchmarks and hemodynamic applications. This is the joint work with Maxim Olshanskii (University of Houston), Alexander Danilov, Alexander Lozovskiy and Victoria Salamatova (INM RAS, MIPT). A.Lozovskiy, M.Olshanskii, V.Salamatova, Yu.Vassilevski. An unconditionally stable semi-implicit FSI finite element method. Comput.Methods Appl.Mech.Engrg., V.297, pp.437-454, 2015 A.Danilov, A.Lozovskiy, M.Olshanskii, Yu.Vassilevski. A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle. Russian J. Numer. Anal. Math. Modelling, V.32, N4, pp.225-236, 2017 A.Lozovskiy, M.Olshanskii, Yu.Vassilevski. A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain. Comput.Methods Appl.Mech.Engrg., V.333, 55-73, 2018

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: Inst. Numerical Mathem RAS

2019-03-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68815

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/