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Volume 41, Issue 1
Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Wei Li, Pengzhan Huang & Yinnian He

DOI: 10.4208/jcm.2104-m2020-0265

J. Comp. Math., 41 (2023), pp. 72-93.

Published online: 2022-11

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  • Abstract

In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the second-order backward differentiation formula for temporal discretization, the second-order Gear's extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

  • Keywords

Fluid-fluid interaction model, Unconditional stability, Second order temporal accuracy, Error estimate.

  • AMS Subject Headings

65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lywinxjst@yeah.net (Wei Li)

hpzh@xju.edu.cn (Pengzhan Huang)

heyn@mail.xjtu.edu.cn (Yinnian He)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-72, author = {Li , WeiHuang , Pengzhan and He , Yinnian}, title = {Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {1}, pages = {72--93}, abstract = {

In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the second-order backward differentiation formula for temporal discretization, the second-order Gear's extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2104-m2020-0265}, url = {http://global-sci.org/intro/article_detail/jcm/21170.html} }
TY - JOUR T1 - Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model AU - Li , Wei AU - Huang , Pengzhan AU - He , Yinnian JO - Journal of Computational Mathematics VL - 1 SP - 72 EP - 93 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2104-m2020-0265 UR - https://global-sci.org/intro/article_detail/jcm/21170.html KW - Fluid-fluid interaction model, Unconditional stability, Second order temporal accuracy, Error estimate. AB -

In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the second-order backward differentiation formula for temporal discretization, the second-order Gear's extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

Li , WeiHuang , Pengzhan and He , Yinnian. (2022). Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model. Journal of Computational Mathematics. 41 (1). 72-93. doi:10.4208/jcm.2104-m2020-0265
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