Optimal mass transport-based adaptive mesh method for phase-field models of two-phase fluid flows

被引：4

作者：

Sulman, Mohamed H. M. ^{[1
]}

机构：

[1] Wright State Univ, Dept Math & Stat, 3640 Col Glenn Highway, Dayton, OH 45435 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 09期

关键词：

Optimal mass transport; Parabolic Monge-Ampere equation; Adaptive mesh; Phase-field model; Incompressible fluids; PARTIAL-DIFFERENTIAL-EQUATIONS; FOURIER-SPECTRAL METHOD; ALLEN-CAHN EQUATION; LAGRANGE MULTIPLIER; MEAN-CURVATURE; EQUIDISTRIBUTION; APPROXIMATION; CONSERVATION; MECHANICS; MIXTURE;

D O I：

10.1016/j.camwa.2016.08.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present an efficient adaptive mesh method for solving phase-field model of a mixture of two-phase incompressible fluid flows. The adaptive mesh is generated by a coordinate transformation that is determined as the solution of the classical problem of the optimal mass transportation, also known as Monge-Kantorovich problem (MKP). The numerical solution of the MKP is computed by taking the gradient of the steady state solution of a parabolic Monge-Ampere equation (PMAE). Several numerical experiments are conducted to demonstrate the performance of the PMAE method for solving phase field models. The numerical results illustrate that the adaptive mesh computed with PMAE method captures well the moving interface of the phase-field function. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：2181 / 2193

页数：13

共 33 条

[1] Convergence of a mass conserving Allen-Cahn equation whose Lagrange multiplier is nonlocal and local [J].

Alfaro, Matthieu ;

Alifrangis, Pierre .

INTERFACES AND FREE BOUNDARIES, 2014, 16 (02) :243-268

[2] MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].

ALLEN, SM ;

CAHN, JW .

ACTA METALLURGICA, 1979, 27 (06) :1085-1095

[3]

Ambrosio L., 2003, LECT NOTES MATH, V1813

[4] Diffuse-interface methods in fluid mechanics [J].

Anderson, DM ;

McFadden, GB ;

Wheeler, AA .

ANNUAL REVIEW OF FLUID MECHANICS, 1998, 30 :139-165

[5] Computational solution of two-dimensional unsteady PDEs using moving mesh methods [J].

Beckett, G ;

Mackenzie, JA ;

Ramage, A ;

Sloan, DM .

JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 182 (02) :478-495

[6]

Benamou JD, 2000, NUMER MATH, V84, P375, DOI 10.1007/s002119900117

[7] A modified phase field approximation for mean curvature flow with conservation of the volume [J].

Brassel, M. ;

Bretin, E. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (10) :1157-1180

[8] POLAR FACTORIZATION AND MONOTONE REARRANGEMENT OF VECTOR-VALUED FUNCTIONS [J].

BRENIER, Y .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (04) :375-417

[9] MOVING MESH GENERATION USING THE PARABOLIC MONGE-AMPERE EQUATION [J].

Budd, C. J. ;

Williams, J. F. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2009, 31 (05) :3438-3465

[10] PHASE FIELD COMPUTATIONS OF SINGLE-NEEDLE CRYSTALS, CRYSTAL-GROWTH, AND MOTION BY MEAN-CURVATURE [J].

CAGINALP, G ;

SOCOLOVSKY, E .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (01) :106-126

← 1 2 3 4 →