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

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/58710 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Release Date

2018

Language

English

Content Metadata

Subject Area

Life Sciences Mathematics Physics

Genre

Workshop/Interactive Format Lecture

Abstract

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). 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