Search Advanced

Networks and Heterogeneous Media

2010, Volume 5, Issue 3: 545-563. doi: 10.3934/nhm.2010.5.545
Previous Article Next Article

Remarks on discretizations of convection terms in Hybrid mimetic mixed methods

  • 1.
    Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugène Bataillon, 34095 Montpellier cedex 5
  • Received: 01 January 2010 Revised: 01 April 2010

  • Primary: 65N12, 65N30, 65M12, 65M60.

  • We present different ways, coming from Finite Volume or Mixed Finite Element frameworks, to discretize convection terms in Hybrid Finite Volume, Mimetic Finite Difference and Mixed Finite Volume methods for elliptic equations. We compare them through several numerical tests, deducing some generic principles, depending on the situation, on the choice of an apropriate method and its parameters. We also present an adaptation to the Navier-Stokes equations, with a numerical tests in the case of the lid-driven cavity.

    Citation: Jérôme Droniou. Remarks on discretizations of convection terms in Hybrid mimetic mixed methods[J]. Networks and Heterogeneous Media, 2010, 5(3): 545-563. doi: 10.3934/nhm.2010.5.545

    Related Papers:

    [1] Jérôme Droniou . Remarks on discretizations of convection terms in Hybrid mimetic mixed methods. Networks and Heterogeneous Media, 2010, 5(3): 545-563. doi: 10.3934/nhm.2010.5.545
    [2] Jinhu Zhao . Natural convection flow and heat transfer of generalized Maxwell fluid with distributed order time fractional derivatives embedded in the porous medium. Networks and Heterogeneous Media, 2024, 19(2): 753-770. doi: 10.3934/nhm.2024034
    [3] Steinar Evje, Kenneth H. Karlsen . Hyperbolic-elliptic models for well-reservoir flow. Networks and Heterogeneous Media, 2006, 1(4): 639-673. doi: 10.3934/nhm.2006.1.639
    [4] Verónica Anaya, Mostafa Bendahmane, David Mora, Ricardo Ruiz Baier . On a vorticity-based formulation for reaction-diffusion-Brinkman systems. Networks and Heterogeneous Media, 2018, 13(1): 69-94. doi: 10.3934/nhm.2018004
    [5] Stefan Berres, Ricardo Ruiz-Baier, Hartmut Schwandt, Elmer M. Tory . An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks and Heterogeneous Media, 2011, 6(3): 401-423. doi: 10.3934/nhm.2011.6.401
    [6] Farman Ali Shah, Kamran, Dania Santina, Nabil Mlaiki, Salma Aljawi . Application of a hybrid pseudospectral method to a new two-dimensional multi-term mixed sub-diffusion and wave-diffusion equation of fractional order. Networks and Heterogeneous Media, 2024, 19(1): 44-85. doi: 10.3934/nhm.2024003
    [7] Xiongfa Mai, Ciwen Zhu, Libin Liu . An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient. Networks and Heterogeneous Media, 2023, 18(4): 1528-1538. doi: 10.3934/nhm.2023067
    [8] Zhangxin Chen . On the control volume finite element methods and their applications to multiphase flow. Networks and Heterogeneous Media, 2006, 1(4): 689-706. doi: 10.3934/nhm.2006.1.689
    [9] Rong Huang, Zhifeng Weng . A numerical method based on barycentric interpolation collocation for nonlinear convection-diffusion optimal control problems. Networks and Heterogeneous Media, 2023, 18(2): 562-580. doi: 10.3934/nhm.2023024
    [10] Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski . An improved homogenization result for immiscible compressible two-phase flow in porous media. Networks and Heterogeneous Media, 2017, 12(1): 147-171. doi: 10.3934/nhm.2017006
  • We present different ways, coming from Finite Volume or Mixed Finite Element frameworks, to discretize convection terms in Hybrid Finite Volume, Mimetic Finite Difference and Mixed Finite Volume methods for elliptic equations. We compare them through several numerical tests, deducing some generic principles, depending on the situation, on the choice of an apropriate method and its parameters. We also present an adaptation to the Navier-Stokes equations, with a numerical tests in the case of the lid-driven cavity.


  • This article has been cited by:

    1. Lorenzo Botti, Daniele A. Di Pietro, Jérôme Droniou, A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device, 2019, 376, 00219991, 786, 10.1016/j.jcp.2018.10.014
    2. Vikendra Singh, A Local Meshless Method for Steady State Convection Dominated Flows, 2017, 14, 0219-8762, 1750067, 10.1142/S0219876217500670
    3. Jerome Droniou, Finite volume schemes for diffusion equations: Introduction to and review of modern methods, 2014, 24, 0218-2025, 1575, 10.1142/S0218202514400041
    4. Claire Chainais-Hillairet, Maxime Herda, Simon Lemaire, Julien Moatti, Long-time behaviour of hybrid finite volume schemes for advection–diffusion equations: linear and nonlinear approaches, 2022, 151, 0029-599X, 963, 10.1007/s00211-022-01289-w
    5. Ophélie Angelini, Konstantin Brenner, Danielle Hilhorst, A finite volume method on general meshes for a degenerate parabolic convection–reaction–diffusion equation, 2013, 123, 0029-599X, 219, 10.1007/s00211-012-0485-5
    6. Daniele A. Di Pietro, Jérôme Droniou, Alexandre Ern, A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes, 2015, 53, 0036-1429, 2135, 10.1137/140993971
    7. Daniele Antonio Di Pietro, Jérôme Droniou, 2020, Chapter 9, 978-3-030-37202-6, 421, 10.1007/978-3-030-37203-3_9
    8. A. Abushaikha, K. Terekhov, Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem, 2024, 45, 1995-0802, 143, 10.1134/S1995080224010025
  • Reader Comments
  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.8

Metrics

Article views(2891) PDF downloads(165) Cited by(8)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog