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The development of an ALE finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian FSI problem

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Abstract

In this paper, we develop a semi-implicit partitioned finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian fluid structure interaction (NNFSI) problem within the arbitrary Lagrangian–Eulerian (ALE) framework. The structure is composed of the elastic solid material. The entire mathematical model consists of the governing equations of the non-Newtonian fluid and the structure, as well as the boundary conditions on the contacting interface. The rheological behavior of non-Newtonian fluid is described according to the power law constitutive equation. The whole system is split into several sub-equations and then appropriate finite element method or discontinuous Galerkin method is employed for the spatial discretizations of them. As for the deformation of the structure and the change of the fluid area and computational mesh, we employ the moving mesh technique to handle them. The problem involving a hot flexible rod fixed on the hot bottom of an irregular pipe is fully investigated. The influences of the fluid inlet velocity and the behavior of the fluid on the deformation of the rod and the temperature distribution are all analyzed.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We are grateful to the support of the National Natural Science Foundation of China (Grant No. 11901051, 11971075), Young Talent Fund of Association for Science and Technology in Shaanxi, China (Grant No. 20220504), the Fundamental Research Funds for the Central Universities, CHD (Grant No. 300102122107) and the International Science and Technology Cooperation Program of Shaanxi Key Research & Development Plan (Grant No. 2019KWZ-08).

Funding

The funding has been received from National Natural Science Foundation of China Grant no. 11901051.

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  1. School of Science, Chang’an University, Xi’an, 710064, China

    Puyang Gao & Xiaolin Hu

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  1. Puyang Gao
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  2. Xiaolin Hu
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Correspondence to Puyang Gao.

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Gao, P., Hu, X. The development of an ALE finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian FSI problem. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01986-0

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