Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model

Year:    2023

Author:    Wei Li, Pengzhan Huang, Yinnian He

Journal of Computational Mathematics, Vol. 41 (2023), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2104-m2020-0265

Journal of Computational Mathematics, Vol. 41 (2023), Iss. 1 : pp. 72–93

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

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

Author Details

Wei Li

Pengzhan Huang

Yinnian He

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