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

ABSTRACT

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.

KEYWORDS:

• Parareal
• finite element
• time-continuous
• non-isothermal flows
• unconditional stability
• superlinearly convergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M12
• 65N15
• 65N30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Science Foundation of China (NSFC) [grant number 61663043].