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

Computer Methods in Applied Mechanics and Engineering
Ju LiuAlison L Marsden

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-α 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 hemodynam...Continue Reading

References

Aug 13, 2013·Journal of Cardiovascular Translational Research·Christopher K ZarinsJames K Min
May 30, 2014·Journal of the Royal Society, Interface·Gang BaoBernhard Schrefler
Mar 30, 2016·International Journal for Numerical Methods in Biomedical Engineering·Vladeta ZmijanovicFranck Nicoud
Dec 10, 2016·Annals of Biomedical Engineering·Adam UpdegroveShawn C Shadden
Jul 27, 2017·International Journal for Numerical Methods in Biomedical Engineering·Cristóbal BertoglioWolfgang A Wall
Dec 7, 2018·Computer Methods in Applied Mechanics and Engineering·Ju Liu, Alison L Marsden
Oct 9, 2019·Journal of Computational Physics·Ju Liu, Alison L Marsden
Sep 29, 2020·International Journal for Numerical Methods in Engineering·Ju LiuZhen Tao

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