The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations

Abstract

We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the generalized-$\alpha$ scheme. The spatiotemporal discretization leads to a block structure of the resulting consistent tangent matrix in the Newton-Raphson procedure. As a generalization of the conventional block preconditioners, a three-level nested block preconditioner is introduced to attain a better representation of the Schur complement, which plays a key role in the overall algorithm robustness and efficiency. This approach provides a flexible, algorithmic way to handle the Schur complement for problems involving multiscale and multiphysics coupling. The solution method is implemented and benchmarked against experimental data from the nozzle challenge problem issued by the US Food and Drug Administration. The robustness, efficiency, and parallel scalability of the proposed technique are then examined in several settings, including moderately high Reynolds number flows and physiological flows with strong resistance effect due to coupled downstream vasculature models. Two patient-specific hemodynamic simulations, covering systemic and pulmonary flows, are performed to further corroborate the efficacy of the proposed methodology.

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Cited by in corpus (7)

• Fluid-structure interaction modeling of blood flow in the pulmonary arteries using the unified continuum and variational multiscale formulation
• Model order reduction of flow based on a modular geometrical approximation of blood vessels
• A continuum and computational framework for viscoelastodynamics: finite deformation linear models
• A note on the accuracy of the generalized-$\alpha$ scheme for the incompressible Navier-Stokes equations
• A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations
• A reduced unified continuum formulation for vascular fluid-structure interaction
• An open-source computational framework for immersed fluid-structure interaction modeling using FEBio and MFEM