Campus Units

Mechanical Engineering

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

8-13-2018

Journal or Book Title

Mathematical Models and Methods in Applied Sciences

DOI

10.1142/S0218202518500537

Abstract

In this work, we analyze the convergence of the recent numerical method for enforcing fluid–structure interaction (FSI) kinematic constraints in the immersogeometric framework for cardiovascular FSI. In the immersogeometric framework, the structure is modeled as a thin shell, and its influence on the fluid subproblem is imposed as a forcing term. This force has the interpretation of a Lagrange multiplier field supplemented by penalty forces, in an augmented Lagrangian formulation of the FSI kinematic constraints. Because of the non-matching fluid and structure discretizations used, no discrete inf-sup condition can be assumed. To avoid solving (potentially unstable) discrete saddle point problems, the penalty forces are treated implicitly and the multiplier field is updated explicitly. In the present contribution, we introduce the term dynamic augmented Lagrangian (DAL) to describe this time integration scheme. Moreover, to improve the stability and conservation of the DAL method, in a recently-proposed extension we projected the multiplier onto a coarser space and introduced the projection-based DAL method. In this paper, we formulate this projection-based DAL algorithm for a linearized parabolic model problem in a domain with an immersed Lipschitz surface, analyze the regularity of solutions to this problem, and provide error estimates for the projection-based DAL method in both the L∞(H1) and L∞(L2) norms. Numerical experiments indicate that the derived estimates are sharp and that the results of the model problem analysis can be extrapolated to the setting of nonlinear FSI, for which the numerical method was originally proposed.

Comments

This is a preprint of an article published in Yu, Yue, David Kamensky, Ming-Chen Hsu, Xin Yang Lu, Yuri Bazilevs, and Thomas J.R. Hughes. "Error estimates for projection-based dynamic augmented Lagrangian boundary condition enforcement, with application to fluid–structure interaction." Mathematical Models and Methods in Applied Sciences (2018): 1-53. DOI: 10.1142/S0218202518500537. © World Scientific Publishing Company. https://www.worldscientific.com/worldscinet/m3as. Posted with permission.

Copyright Owner

World Scientific Publishing Company

Language

en

File Format

application/pdf

Published Version

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