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Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model

  • Received: 01 March 2020 Revised: 01 June 2020
  • Primary: 65M12, 35k20; Secondary: 35K35

  • In this paper, we construct a modular grad-div stabilization method for the Navier-Stokes/Darcy model, which is based on the first order Backward Euler scheme. This method does not enlarge the accuracy of numerical solution, but also can improve mass conservation and relax the influence of parameters. Herein, we give stability analysis and error estimations. Finally, by some numerical experiment, the scheme our proposed is shown to be valid.

    Citation: Jiangshan Wang, Lingxiong Meng, Hongen Jia. Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model[J]. Electronic Research Archive, 2020, 28(3): 1191-1205. doi: 10.3934/era.2020065

    Related Papers:

  • In this paper, we construct a modular grad-div stabilization method for the Navier-Stokes/Darcy model, which is based on the first order Backward Euler scheme. This method does not enlarge the accuracy of numerical solution, but also can improve mass conservation and relax the influence of parameters. Herein, we give stability analysis and error estimations. Finally, by some numerical experiment, the scheme our proposed is shown to be valid.



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