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 journalArticlepeer-review

16 Scopus citations


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
StatePublished - Jul 1 2017

Bibliographical note

Funding Information:
D. Schillinger gratefully acknowledges support from the National Science Foundation through grant CISE-1565997 and the NSF CAREER Award No. 1651577. We also acknowledge the Minnesota Supercomputing Institute (MSI) of the University of Minnesota for providing computing resources that have contributed to the research results reported within this paper (https://www.msi.umn.edu/). We thank Dr.?Andr? Massing for his help with implementing conforming interfaces in FEniCS, and Dr.?David Kamensky for insightful discussions on stabilization techniques.

Publisher Copyright:
© 2017 Elsevier B.V.

Copyright 2017 Elsevier B.V., All rights reserved.


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

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