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A One-Dimensional Coarse Preconditioner for Three-Dimensional Unsteady Incompressible Navier-Stokes Flows in Patient-Specific Arteries

Yingzhi Liu,Fenfen Qi,Xiaojing Cai

Published 2023 in SIAM Journal on Scientific Computing

ABSTRACT

. Numerical simulation of blood flows in patient-specific arteries is becoming an important tool in understanding 5 vascular diseases and surgery planning. Depending on the branching geometry and the patient parameters, the flow can be quite 6 complicated with local vortex structures and rotations, but the principal component of the flow is always along the centerline of 7 the artery. Based on this observation, we introduce a new two-level domain decomposition method for unsteady incompressible 8 Navier-Stokes equations in three-dimensional complex patient-specific arteries, and the key component of the preconditioner is a 9 parameterized one-dimensional unsteady Navier-Stokes or Stokes coarse problem defined along the centerline of the artery. The 10 one-dimensional preconditioner and some overlapping three-dimensional subdomain preconditioners are combined additively to 11 form the two-level method via interpolations using radial basis functions. The most important feature of the method is that 12 the cost of solving the coarse problem is nearly neglectable compared with the subdomain solver. The blood flow is modeled 13 by the unsteady incompressible Navier-Stokes equations with resistance outflow boundary conditions discretized by a stabilized 14 finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. Numerical 15 experiments indicate that the proposed method is highly effective and robust for complex arteries with many branches, in other 16 words, the numbers of linear and nonlinear iterations change very little when the mesh is refined or the number of subdomains 17 is increased or the number of arterial branches is increased. 18

PUBLICATION RECORD

  • Publication year

    2023

  • Venue

    SIAM Journal on Scientific Computing

  • Publication date

    2023-07-13

  • Fields of study

    Medicine, Computer Science, Engineering

  • Identifiers
    DOI 10.1137/22m1496773
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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