Yu. Vassilevski | Stable numerical schemes for modelling hemodynamic flows in time-dependent domains
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2022-08-01

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Yuri V. Vassilevski (Marchuk Institute of Numerical Mathematics,  Sechenov University) 
Stable numerical schemes for modelling hemodynamic flows in time-dependent domains

We present a unified numerical approach to finite-element modelling of incompressible flows in time-dependent domains. The approach features relatively large (independent of mesh size) time steps, solution of one linear system per time step, and relatively coarse computational meshes in space. The approach is monolithic and allows standard 𝑃2 − 𝑃1 (Taylor–Hood) finite element spaces. It is applicable to the Navier-Stokes equations in time-dependent domains, the fluid-structure interaction (FSI) problems, and the fluid-porous structure interaction (FPSI) problems. The properties of the schemes are shown on several benchmarks and hemodynamic applications.
References
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