A UNIFIED STABILIZED FINITE VOLUME METHOD FOR STOKES AND DARCY EQUATIONS

被引：4
|
作者：
Boukabache, Akram [1 ]
Kechkar, Nasserdine [2 ]
机构：
[1] Univ Mohamed Sedd Benyahia, Lab Pure & Appl Math, Jijel, Algeria
[2] Univ Freres Mentouri, Dept Math, Constantine, Algeria
来源：
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2019年 / 56卷 / 04期
关键词：
finite volumes; collocated discretizations; Stokes equation; Darcy equation; stabilized methods; ELEMENT; FORMULATIONS;
D O I：
10.4134/JKMS.j180641
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present and analyze a cell-centered collocated finite volume scheme for incompressible flows to compute solutions simultaneous to Stokes and Darcy equations by applying a pressure jump stabilization term to avoid locking. We prove that the new stabilized FV formulation satisfies a discrete inf-sup condition and error estimates for both problems. Finally, we present some numerical examples confirming this analysis.
引用
收藏
页码：1083 / 1112
页数：30
相关论文
共 50 条
  • [1] A unified stabilized method for Stokes' and Darcy's equations
    Burman, Erik
    Hansbo, Peter
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 198 (01) : 35 - 51
  • [2] A Discontinuous Finite Volume Method for the Darcy-Stokes Equations
    Yin, Zhe
    Jiang, Ziwen
    Xu, Qiang
    [J]. JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [3] A stabilized finite volume method for the evolutionary Stokes-Darcy system
    Li, Yi
    Hou, Yanren
    Li, Rui
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (02) : 596 - 613
  • [4] A unified stabilized mixed finite element method for coupling Stokes and Darcy flows
    Rui, Hongxing
    Zhang, Ran
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2009, 198 (33-36) : 2692 - 2699
  • [5] A Stabilized Finite Volume Element Method for Stationary Stokes-Darcy Equations Using the Lowest Order
    Wu, Yanyun
    Mei, Liquan
    Qiu, Meilan
    Chu, Yuchuan
    [J]. INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2020, 17 (08)
  • [6] UNIFIED STABILIZED FINITE ELEMENT FORMULATIONS FOR THE STOKES AND THE DARCY PROBLEMS
    Badia, Santiago
    Codina, Ramon
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) : 1971 - 2000
  • [7] A stabilized finite volume element method for a coupled Stokes-Darcy problem
    Li, Rui
    Li, Jian
    He, Xiaoming
    Chen, Zhangxin
    [J]. APPLIED NUMERICAL MATHEMATICS, 2018, 133 : 2 - 24
  • [8] A new stabilized finite volume method for the stationary Stokes equations
    Li, Jian
    Chen, Zhangxin
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2009, 30 (02) : 141 - 152
  • [9] A new stabilized finite volume method for the stationary Stokes equations
    Jian Li
    Zhangxin Chen
    [J]. Advances in Computational Mathematics, 2009, 30 : 141 - 152
  • [10] ANALYSIS OF A STABILIZED FINITE VOLUME METHOD FOR THE TRANSIENT STOKES EQUATIONS
    Shen, Lihua
    Li, Jian
    Chen, Zhangxin
    [J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2009, 6 (03) : 505 - 519
12345