InterPore2023

A Lagrange multiplier method for the fully dynamic Navier-Stokes - Biot system

25 May 2023, 09:45

15m

Oral Presentation (MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes MS07

Speaker

Ivan Yotov (University of Pittsburgh)

Description

We develop a mixed finite element computational model for the interaction between a free fluid and a poroelastic medium . The free fluid flow is governed by the time-dependent incompressible Navier-Stokes equations, while the poroelastic region is governed by the Biot system. A Lagrange multiplier method is employed to impose weakly the continuity of flux. Under a small data condition, existence, uniqueness, and stability of the semi-discrete continuous-in-time and fully discrete formulations are proved. We further establish error estimates for the fully discrete method. A series of numerical experiments are presented to verify the theoretical convergence rates and illustrate the applicability of the method to modeling arterial blood flows.