Spectral numerical schemes for time-dependent convection with viscosity dependent on temperature |
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Affiliation: | 1. Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UC3M), Nicolás Cabrera, 13-15, Campus Cantoblanco UAM, 28049 Madrid, Spain;2. Departamento de Matemáticas de la Universidad Autónoma de Madrid, Facultad de Ciencias, Módulo 17, 28049 Madrid, Spain;1. School of Mathematical Sciences, Shandong Normal University, Ji’nan 250014, PR China;2. Research Center on Logistics optimization and Prediction of Engineering Technology, Ji’nan, Shandong 250014, PR China;1. Nonlinear Electronics Laboratory, Center for Physical Sciences and Technology, LT-01108 Vilnius, Lithuania;2. Department of Physics, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania;1. Universidade Nove de Julho, Departamento de Informática, Rua Guaranésia, n. 425, CEP 02112-000, São Paulo, SP, Brazil;2. Universidade Presbiteriana Mackenzie, Escola de Engenharia, Pós-Graduação em Engenharia Elétrica, Rua da Consolação, n. 896, CEP 01302-907, São Paulo, SP, Brazil;3. Universidade de São Paulo, Escola Politécnica, Departamento de Engenharia de Telecomunicações e Controle, Av. Prof. Luciano Gualberto, travessa 3, n. 380, CEP 05508-900, São Paulo, SP, Brazil |
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Abstract: | This article proposes spectral numerical methods to solve the time evolution of convection problems with viscosity strongly dependent on temperature at infinite Prandtl number. Although we verify the proposed techniques solely for viscosities that depend exponentially on temperature, the methods are extensible to other dependence laws. The set-up is a 2D domain with periodic boundary conditions along the horizontal coordinate which introduces a symmetry in the problem. This is the O(2) symmetry, which is particularly well described by spectral methods and motivates the use of these methods in this context. We examine the scope of our techniques by exploring transitions from stationary regimes towards time dependent regimes. At a given aspect ratio, stable stationary solutions become unstable through a Hopf bifurcation, after which the time-dependent regime is solved by the spectral techniques proposed in this article. |
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Keywords: | Spectral semi-implicit method Numerical analysis Convection with viscosity dependent on temperature Infinite Prandtl number |
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