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A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition

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Abstract

In this paper, we propose and analyze the parallel Robin–Robin domain decomposition method based on the modified characteristic finite element method for the time-dependent dual-porosity-Navier–Stokes model with the Beavers–Joseph interface condition. For the coupling terms, we treat them in an explicit manner which takes advantage of information obtained in previous time steps to construct a non-iteration domain decomposition method. By this means, two single dual-porosity equations and a single Navier–Stokes equation are needed to solve at each time. In particular, we solve the Navier–Stokes equation by the modified characteristic finite element method, which avoids the computational inefficiency caused by the nonlinear convection term. Furthermore, we prove the error convergence of solutions by mathematical induction, whose proof implies the uniform \(L^{\infty }\)-boundedness of the fully discrete velocity solution in conduit flow. Finally, some numerical examples are presented to show the effectiveness and efficiency of the proposed method.

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Acknowledgements

This work is partially supported by the Natural Science Foundation of China under Grant No. 11771348 and No. 11771259 and the Major Research and Development Program of China under Grant No. 2016YFB0200901. It is also supported by the China Scholarship Council Grant 202006280440 and the special support program to develop innovative talents in the region of Shaanxi province, innovation team on computationally efficient numerical methods based on new energy problems in Shaanxi province, and innovation team project of Shaanxi Provincial Department of Education (No. 21JP013).

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  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Luling Cao & Yinnian He

  2. Department of Mathematics, Shaanxi University of Science and Technology, Xi’an, 710021, China

    Jian Li

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  1. Luling Cao
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Cao, L., He, Y. & Li, J. A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition. J Sci Comput 90, 16 (2022). https://doi.org/10.1007/s10915-021-01674-x

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