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The second order projection method in time for the time-dependent natural convection problem

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Abstract

We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time.

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Authors and Affiliations

  1. Henan Polytechnic University, Heping St, Jiefang, Jiaozuo, Henan, P.R. China

    Yanxia Qian & Tong Zhang

  2. Departamento de Matemática, Universidade Federal do Paraná, Centro Politácnico, Curitiba, 81531-980, P.R. Brazil

    Tong Zhang

Authors
  1. Yanxia Qian
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  2. Tong Zhang
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Correspondence to Yanxia Qian.

Additional information

The research has been supported by CAPES and CNPq of Brazil (No. 88881.068004/2014.01), the NSF of China (No. 11301157), and the FDYS of Henan Polytechnic University (J2015-05).

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Qian, Y., Zhang, T. The second order projection method in time for the time-dependent natural convection problem. Appl Math 61, 299–315 (2016). https://doi.org/10.1007/s10492-016-0133-y

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