
 
Isogeometric Analysis of a Phase Field Model for Darcy Flows with Discontinuous Data 
 
Citation： 
Luca DED`E,Alfio QUARTERONI.Isogeometric Analysis of a Phase Field Model for Darcy Flows with Discontinuous Data[J].Chinese Annals of Mathematics B,2018,39(3):487~512 
Page view： 1010
Net amount： 934 
Authors： 
Luca DED`E; Alfio QUARTERONI 
Foundation： 
This work has been partially funded by the INdAMGNCS
Project 2017 "Modellistica numerica di fenomeni idro/geomeccanici
per la simulazione di eventi sismici". 


Abstract： 
The authors consider a phase field model for Darcy flows with
discontinuous data in porous media; specifically, they adopt the
HeleShawCahnHillard equations of [Lee, Lowengrub, Goodman, {\it
Physics of Fluids}, 2002] to model flows in the HeleShaw cell
through a phase field formulation which incorporates discontinuities
of physical data, namely density and viscosity, across interfaces.
For the spatial approximation of the problem, the authors use
NURBSbased isogeometric analysis in the framework of the Galerkin
method, a computational framework which is particularly advantageous
for the solution of high order partial differential equations and
phase field problems which exhibit sharp but smooth interfaces. In
this paper, the authors verify through numerical tests the sharp
interface limit of the phase field model which in fact leads to an
internal discontinuity interface problem; finally, they show the
efficiency of isogeometric analysis for the numerical approximation
of the model by solving a benchmark problem, the socalled ``rising
bubble" problem. 
Keywords： 
Darcy flows, Phase field, HeleShaw cell, CahnHilliard equation,Sharp interface limit, Isogeometric analysis 
Classification： 
65L60, 74S05, 80A22 

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