A diffuse interface method for the Navier–Stokes/Darcy equations

 Perfusion profile for a patient-specific human liver based on MRI scans

Stein K.F. Stoter, Peter Müller, Luca Cicalese, Massimiliano Tuveri, Dominik Schillinger, Thomas J.R. Hughes

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We present a diffuse interface method for coupling free and porous-medium-type flows modeled by the Navier–Stokes and Darcy equations. Its essential component is a diffuse geometry model generated from the phase-field solution of a separate initial boundary value problem that is based on the Allen–Cahn equation. Phase-field approximations of the interface and its gradient are then employed to transfer all interface terms in the coupled variational flow formulation into volumetric terms. This eliminates the need for an explicit interface parametrization between the two flow regimes. We illustrate accuracy and convergence for a series of benchmark examples, using standard low-order stabilized finite element discretizations. Our diffuse interface method is particularly attractive for coupled flow analysis on imaging data with complex implicit interfaces, where procedures for deriving explicit surface parametrizations constitute a significant bottleneck. We demonstrate the potential of our method to establish seamless imaging-through-analysis workflows by computing a perfusion profile for a full-scale 3D human liver based on MRI scans.

Original languageEnglish (US)
Pages (from-to)70-102
Number of pages33
JournalComputer Methods in Applied Mechanics and Engineering
Volume321
DOIs
StatePublished - Jul 1 2017

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liver
Liver
Imaging techniques
profiles
Boundary value problems
Porous materials
Geometry
boundary value problems
Magnetic Resonance Imaging
formulations
gradients
geometry
approximation

Keywords

  • Allen–Cahn equation
  • Diffuse interface method
  • Imaging data
  • Liver
  • Navier–Stokes/Darcy coupling
  • Phase-field approximation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

A diffuse interface method for the Navier–Stokes/Darcy equations :  Perfusion profile for a patient-specific human liver based on MRI scans. / Stoter, Stein K.F.; Müller, Peter; Cicalese, Luca; Tuveri, Massimiliano; Schillinger, Dominik; Hughes, Thomas J.R.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 321, 01.07.2017, p. 70-102.

Research output: Contribution to journalArticle

Stoter, Stein K.F. ; Müller, Peter ; Cicalese, Luca ; Tuveri, Massimiliano ; Schillinger, Dominik ; Hughes, Thomas J.R. / A diffuse interface method for the Navier–Stokes/Darcy equations :  Perfusion profile for a patient-specific human liver based on MRI scans. In: Computer Methods in Applied Mechanics and Engineering. 2017 ; Vol. 321. pp. 70-102.
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