Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid–thin structure interaction analysis, with application to heart valve modeling

• Published in: Computers & mathematics with applications (1987) Vol. 74; no. 9; pp. 2068 - 2088
• Main Authors: Kamensky, David, Evans, John A., Hsu, Ming-Chen, Bazilevs, Yuri
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 01.11.2017; Elsevier BV
• Subjects: Computational fluid dynamics; Computer simulation; Finite cell method; Fluid dynamics; Fluid–structure interaction; Heart valves; Immersogeometric analysis; Integrators; Isogeometric analysis; Iterative methods; Lagrange multiplier; Projection-based stabilization; Saddle points; Simulation; Sketches; Stabilization; Isogeometric analysis; Finite cell method; Fluid–structure interaction; Projection-based stabilization; Immersogeometric analysis; Heart valves; Fluid; structure interaction
• ISSN: 0898-1221; 1873-7668; 1873-7668
• DOI: 10.1016/j.camwa.2017.07.006

This paper discusses a method of stabilizing Lagrange multiplier fields used to couple thin immersed shell structures and surrounding fluids. The method retains essential conservation properties by stabilizing only the portion of the constraint orthogonal to a coarse multiplier space. This stabilization can easily be applied within iterative methods or semi-implicit time integrators that avoid directly solving a saddle point problem for the Lagrange multiplier field. Heart valve simulations demonstrate applicability of the proposed method to 3D unsteady simulations. An appendix sketches the relation between the proposed method and a high-order-accurate approach for simpler model problems.