TY - JOUR
T1 - A diffuse interface method for the Navier–Stokes/Darcy equations
T2 - Perfusion profile for a patient-specific human liver based on MRI scans
AU - Stoter, Stein K.F.
AU - Müller, Peter
AU - Cicalese, Luca
AU - Tuveri, Massimiliano
AU - Schillinger, Dominik
AU - Hughes, Thomas J.R.
N1 - .
PY - 2017/7/1
Y1 - 2017/7/1
N2 - 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.
AB - 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.
KW - Allen–Cahn equation
KW - Diffuse interface method
KW - Imaging data
KW - Liver
KW - Navier–Stokes/Darcy coupling
KW - Phase-field approximation
UR - http://www.scopus.com/inward/record.url?scp=85018410925&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2017.04.002
DO - 10.1016/j.cma.2017.04.002
M3 - Article
AN - SCOPUS:85018410925
SN - 0045-7825
VL - 321
SP - 70
EP - 102
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -