A Decoupled and Iterative Finite Element Method for Generalized Boussinesq Equations

Abstract

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.

Department(s)

Mathematics and Statistics

Comments

National Natural Science Foundation of China, Grant 11871139

Keywords and Phrases

Decoupled iterative scheme; Error analysis; Finite element method; Steady-state generalized Boussinesq equations

International Standard Serial Number (ISSN)

0898-1221

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Elsevier, All rights reserved.

Publication Date

01 Jun 2022

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