An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension

被引：19

作者：

Alharbi, Abdulghani ^{[1
,2
]}

Naire, Shailesh ^{[2
]}

机构：

[1] Taibah Univ, Dept Math, Univ Rd,POB 344, Medina, Saudi Arabia

[2] Keele Univ, Sch Comp & Math, Keele ST5 5BG, Staffs, England

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 356卷

关键词：

Thin film flows; Surface tension; Fingering instability; Adaptive moving mesh; r-adaptive method; Moving Mesh PDEs (MMPDEs); PARTIAL-DIFFERENTIAL-EQUATIONS; INDUCED FINGERING PHENOMENA; INSOLUBLE SURFACTANT; INCLINED PLANE; LADEN DROP; STABILITY; DRIVEN; ALGORITHM; DYNAMICS; SCHEMES;

D O I：

10.1016/j.cam.2019.02.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we extend our previous work (Alharbi and Naire, 2017) on a one-dimensional r-adaptive moving mesh technique based on a mesh density function and moving mesh partial differential equations (MMPDEs) to two dimensions. As a test problem, we consider the gravity-driven thin film flow down an inclined and pre-wetted plane including surface tension and a moving contact line. This technique accurately captures and resolves the moving contact line and associated fingering instability. Moreover, the computational effort is hugely reduced in comparison to a fixed uniform mesh. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：219 / 230

页数：12

共 42 条

[1] An adaptive moving mesh method for thin film flow equations with surface tension [J].

Alharbi, Abdulghani ;

Naire, Shailesh .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 319 :365-384

[2] Finite element approximation of a fourth order nonlinear degenerate parabolic equation [J].

Barrett, JW ;

Blowey, JF ;

Garcke, H .

NUMERISCHE MATHEMATIK, 1998, 80 (04) :525-556

[3] Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem [J].

Beckett, G ;

Mackenzie, JA .

APPLIED NUMERICAL MATHEMATICS, 2000, 35 (02) :87-109

[4]

Bernis F., 1995, Free Boundary Problems: Theory and Applications, V323, P40

[5]

Bertozzi A.L., 1998, Notices Amer. Math. Soc, V45, P689

[6] Linear stability and transient growth in driven contact lines [J].

Bertozzi, AL ;

Brenner, MP .

PHYSICS OF FLUIDS, 1997, 9 (03) :530-539

[7] ALGORITHM 731 - A MOVING-GRID INTERFACE FOR SYSTEMS OF ONE-DIMENSIONAL TIME-DEPENDENT PARTIAL-DIFFERENTIAL EQUATIONS [J].

BLOM, JG ;

ZEGELING, PA .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1994, 20 (02) :194-214

[8] USING KRYLOV METHODS IN THE SOLUTION OF LARGE-SCALE DIFFERENTIAL-ALGEBRAIC SYSTEMS [J].

BROWN, PN ;

HINDMARSH, AC ;

PETZOLD, LR .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (06) :1467-1488

[9] Monge-Ampere based moving mesh methods for numerical weather prediction, with applications to the Eady problem [J].

Budd, C. J. ;

Cullen, M. J. P. ;

Walsh, E. J. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 236 :247-270

[10] 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

← 1 2 3 4 5 →