The Navier-Stokes-$\omega$/Navier-Stokes-$\omega$ Model for Fluid-Fluid Interaction Using an Unconditionally Stable Finite Element Scheme
Year: 2025
Author: Qinghui Wang, Pengzhan Huang, Yinnian He
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 178–201
Abstract
In this article, for solving fluid-fluid interaction problem, we consider a Navier-Stokes-$ω$/Navier-Stokes-$ω$ model, which includes two Navier-Stokes-$ω$ equations coupled by some nonlinear interface conditions. Based on an auxiliary variable, we propose a fully discrete, decouple finite element scheme. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. Moreover, the proposed scheme is shown to be unconditionally stable. Then, we establish error estimate of the numerical solution. Finally, with a series of numerical experiments we illustrate the stability and effectiveness of the proposed scheme and its ability to capture basic phenomenological features of the fluid-fluid interaction.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1009
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 178–201
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Navier-Stokes-$ω$ model fluid-fluid interaction auxiliary variable unconditional stability.
Author Details
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https://doi.org/10.3934/era.2025111 [Citations: 0]