A Decoupled and Iterative Finite Element Method for Generalized Boussinesq Equations
In this work, a decoupled and iterative finite element method is developed and analyzed for steady-state generalized Boussinesq equations, in which both the viscosity and thermal conductivity depend on the temperature. By utilizing the solutions obtained in the previous iteration step, the coupled system is reduced to Navier-Stokes equations with temperature-dependent viscosity and a linearized convection-diffusion equation, which can be solved in parallel. The well-posedness and stability of the scheme are proved. Finite element errors and iterative errors are analyzed for the cases of both temperature-dependent and temperature-independent thermal conductivity. Numerical examples are provided to demonstrate the convergence, accuracy and applicability of the proposed method.
Y. Hou et al., "A Decoupled and Iterative Finite Element Method for Generalized Boussinesq Equations," Computers and Mathematics with Applications, vol. 115, pp. 14 - 25, Elsevier, Jun 2022.
The definitive version is available at https://doi.org/10.1016/j.camwa.2022.04.003
Mathematics and Statistics
Keywords and Phrases
Decoupled iterative scheme; Error analysis; Finite element method; Steady-state generalized Boussinesq equations
International Standard Serial Number (ISSN)
Article - Journal
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01 Jun 2022