A new multipoint flux approximation method with a quasi-local stencil (MPFA-QL) for the simulation of diffusion problems in anisotropic and heterogeneous media

被引：19

作者：

Contreras, Fernando R. L. ^{[1
]}

Lyra, Paulo R. M. ^{[2
]}

de Carvalho, Darlan K. E. ^{[2
]}

机构：

[1] Univ Fed Pernambuco, NT CAA, Rodovia BR 104 KM 59 S-N, BR-55002970 Caruaru, PE, Brazil

[2] Univ Fed Pernambuco, Dept Engn Mecan, Av Acad Helio Ramos S-N, BR-50670901 Recife, PE, Brazil

来源：

APPLIED MATHEMATICAL MODELLING | 2019年 / 70卷

关键词：

Diffusion equation; Anisotropic and heterogeneous media; Linearity-preserving interpolation; MPFA-QL; FINITE-VOLUME SCHEMES; EQUATIONS; DISCRETIZATION;

D O I：

10.1016/j.apm.2019.01.033

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we present a new linear cell-centered finite volume multipoint flux approximation (MPFA-QL) scheme for discretizing diffusion problems on general polygonal meshes. This scheme uses a quasi-local stencil, based upon the conormal decomposition, to approximate the control face flux when solving the steady state diffusion problem, being able to reproduce piecewise linear solutions exactly and it is very robust when dealing with heterogeneous and highly anisotropic media and severely distorted meshes. In our linear scheme, we first construct the one-sided fluxes on each control surface independently and then a unique flux expression is obtained by a convex combination of the one-sided fluxes. The unknown values at the vertices that define a control surface are interpolated by means of a linearity-preserving interpolation procedure, considering control volumes surrounding these vertices. To show the potential of the MPFA-QL scheme, we solve some benchmark using triangular and quadrilateral meshes and we compare our scheme with other numerical formulations found in literature. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：659 / 676

页数：18

共 34 条

[1] A compact multipoint flux approximation method with improved robustness [J].

Aavatsmark, I. ;

Eigestad, G. T. ;

Mallison, B. T. ;

Nordbotten, J. M. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (05) :1329-1360

[2] Convergence of a symmetric MPFA method on quadrilateral grids [J].

Aavatsmark, I. ;

Eigestad, G. T. ;

Klausen, R. A. ;

Wheeler, M. F. ;

Yotov, I. .

COMPUTATIONAL GEOSCIENCES, 2007, 11 (04) :333-345

[3] Discretization on unstructured grids for inhomogeneous, anisotropic media. Part II: Discussion and numerical results [J].

Aavatsmark, I ;

Barkve, T ;

Boe, O ;

Mannseth, T .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 19 (05) :1717-1736

[4] An introduction to multipoint flux approximations for quadrilateral grids [J].

Aavatsmark, I .

COMPUTATIONAL GEOSCIENCES, 2002, 6 (3-4) :405-432

[5]

Agelas L., 2010, INT J FINITE, V7

[6]

Agelas L., 2008, Finite Volume for Complex Applications V, P35

[7]

[Anonymous], 2009, INT J FINITE

[8] An efficient cell-centered diffusion scheme for quadrilateral grids [J].

Basko, M. M. ;

Maruhn, J. ;

Tauschwitz, An. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (06) :2175-2193

[9]

Bear J., 2013, DOVER CIVIL MECH ENG

[10]

Bergman TL., 2011, Introduction to heat transfer, DOI DOI 10.1016/J.APPLTHERMALENG.2011.03.022

← 1 2 3 4 →