Vascular fluid-structure interaction: unified continuum formulation, image-based mesh generation pipeline, and scalable fully implicit solver technology
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We propose a computational framework for vascular fluid-structure interaction (FSI), focusing on biomechanical modeling, geometric modeling, and solver technology. The biomechanical model is constructed based on the unified continuum formulation. We highlight that the chosen time integration scheme differs from existing implicit FSI integration methods in that it is indeed second-order accurate, does not suffer from the overshoot phenomenon, and optimally dissipates high-frequency modes in both subproblems. We propose a pipeline for generating subject-specific meshes for FSI analysis for anatomically realistic geometric modeling. Unlike most existing methodologies that operate directly on the wall surface mesh, our pipeline starts from the image segmentation stage. With high-quality surface meshes obtained, the volumetric meshes are then generated, guaranteeing a boundary-layered mesh in the fluid subdomain and a matching mesh across the fluid-solid interface. In the last, we propose a combined suite of nonlinear and linear solver technologies. Invoking a segregated algorithm within the Newton-Raphson iteration, the problem reduces to solving two linear systems in the multi-corrector stage. The first linear system can be addressed by the algebraic multigrid (AMG) method. The matrix related to the balance equations presents a two-by-two block structure in both subproblems. Using the Schur complement reduction (SCR) technique reduces the problem to solving matrices of smaller sizes of the elliptic type, and the AMG method again becomes a natural candidate. The benefit of the unified formulation is demonstrated in parallelizing the solution algorithms as the number of unknowns matches in both subdomains. We use the Greenshields-Weller benchmark as well as a patient-specific vascular model to demonstrate the robustness, efficiency, and scalability of the overall FSI solver technology.
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