Convergence analysis of a parareal-in-time algorithm for the incompressible non-isothermal flows

This paper presents and analyzes a parareal-in-time scheme for the incompressible non-isothermal Navier-Stokes equations with Boussinesq approximation. Standard finite element method is adopted for the spatial discretization.The proposed algorithm is proved to be unconditional stability. The converg...

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Bibliographic Details
Published in:International journal of computer mathematics 2019-07, Vol.96 (7), p.1398-1415
Main Authors: Miao, Zhen, Jiang, Yao-Lin, Yang, Yun-Bo
Format: Article
Language:English
Subjects:
Algorithms
Boussinesq approximation
Computational fluid dynamics
Convergence
finite element
Finite element analysis
Finite element method
Fluid flow
Incompressible flow
Iterative methods
Mathematical analysis
non-isothermal flows
Parareal
superlinearly convergence
time-continuous
unconditional stability
Viscosity
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Summary:This paper presents and analyzes a parareal-in-time scheme for the incompressible non-isothermal Navier-Stokes equations with Boussinesq approximation. Standard finite element method is adopted for the spatial discretization.The proposed algorithm is proved to be unconditional stability. The convergence factor of iteration error for the velocity and temperature is given at time-continuous case. It theoretically demonstrates the superlinearly convergence of the parareal iteration combined with finite element method for incompressible non-isothermal flows. Finally, several numerical experiments that confirm feasibility and applicability of the algorithm perform well as expected.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2018.1498484