A closed-loop lumped parameter network (LPN) coupled to a 3D domain is a powerful tool that can be used to model the global dynamics of the circulatory system. Coupling a 0D LPN to a 3D CFD domain is a numerically challenging problem, often associated with instabilities, extra computational cost, and loss of modularity. A computationally efficient finite element framework has been recently proposed that achieves numerical stability without sacrificing modularity . This type of coupling introduces new challenges in the linear algebraic equation solver (LS), producing an strong coupling between flow and pressure that leads to an ill-conditioned tangent matrix. In this paper we exploit this strong coupling to obtain a novel and efficient algorithm for the linear solver (LS). We illustrate the efficiency of this method on several large-scale cardiovascular blood flow simulation problems.
- Bioengineering Division
An Efficient Preconditioner for Linear System Solution in Multi-Domain Modeling of the Circulatory System
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Moghadam, ME, Bazilevs, Y, Hsia, T, & Marsden, A. "An Efficient Preconditioner for Linear System Solution in Multi-Domain Modeling of the Circulatory System." Proceedings of the ASME 2013 Summer Bioengineering Conference. Volume 1A: Abdominal Aortic Aneurysms; Active and Reactive Soft Matter; Atherosclerosis; BioFluid Mechanics; Education; Biotransport Phenomena; Bone, Joint and Spine Mechanics; Brain Injury; Cardiac Mechanics; Cardiovascular Devices, Fluids and Imaging; Cartilage and Disc Mechanics; Cell and Tissue Engineering; Cerebral Aneurysms; Computational Biofluid Dynamics; Device Design, Human Dynamics, and Rehabilitation; Drug Delivery and Disease Treatment; Engineered Cellular Environments. Sunriver, Oregon, USA. June 26–29, 2013. V01AT13A014. ASME. https://doi.org/10.1115/SBC2013-14392
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