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  • Open Access

    ARTICLE

    Application of the Fictitious Domain Method for Navier-Stokes Equations

    Almas Temirbekov1, Zhadra Zhaksylykova2,*, Yerzhan Malgazhdarov3, Syrym Kasenov1

    CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 2035-2055, 2022, DOI:10.32604/cmc.2022.027830 - 18 May 2022

    Abstract To apply the fictitious domain method and conduct numerical experiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different values of the iterative parameter τ and the small parameter ε are presented. A study of the auxiliary problem of the fictitious domain method for Navier-Stokes equations with continuation into a fictitious subdomain by higher coefficients with a small parameter is carried out. A generalized solution of the auxiliary problem of the fictitious domain method with continuation by higher coefficients with a small parameter is determined. After… More >

  • Open Access

    ARTICLE

    Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

    Andrew Lundberg1, Pengtao Sun1,∗, Cheng Wang2, Chen-song Zhang3

    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 35-62, 2019, DOI:10.32604/cmes.2019.04804

    Abstract The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated. More >

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