DeepAI AI Chat
Log In Sign Up

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

11/25/2019
by   Ju Liu, et al.
0

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 hemodynamic simulations, covering systemic and pulmonary flows, are performed to further corroborate the efficacy of the proposed methodology.

READ FULL TEXT

page 3

page 25

page 26

page 28

page 29

page 30

09/16/2020

Recursive formulation and parallel implementation of multiscale mixed methods

Multiscale methods for second order elliptic equations based on non-over...
07/03/2020

A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

We study a decoupling iterative algorithm based on domain decomposition ...
11/16/2021

Block preconditioning methods for asymptotic preserving scheme arising in anisotropic elliptic problems

Efficient and robust iterative solvers for strong anisotropic elliptic e...
12/14/2020

A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD

We present a scalable block preconditioning strategy for the trace syste...