期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 28, 期 12, 页码 2457-2509出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202518500537
关键词
Immersogeometric method; fluid-structure interaction (FSI); augmented Lagrangian method; parabolic initial-boundary value problem; sub-optimal error estimates; Lipschitz domain
资金
- National Science Foundation [DMS-1620434]
- AFOSR [FA9550-16-1-0131]
- NIH/NHLBI Award [R01HL129077]
- ONR [N00014-17-1-2119, N00014-13-1-0500]
- Lakehead University [10-50-16422410, 10-50-16422409]
- NSERC [10-50-16420120]
- Simons collaboration Grant [360504]
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 supple-mented 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-infinity (H-1) and L-infinity (L-2) 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.
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