A decoupled and iterative finite element method for generalized Boussinesq equations. (1st June 2022)

• Record Type: Journal Article
• Authors: Hou, Yuanyuan; Yan, Wenjing; Li, Maojun; He, Xiaoming
• Is Part Of: Computers & mathematics with applications. Volume 115(2022)
• Page Start: 14
• Page End: 25
• Publication Date: 2022-06-01
• Subjects: Steady-state generalized Boussinesq equations -- Decoupled iterative scheme -- Finite element method -- Error analysis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.04.003
• Languages: English
• ISSNs: 0898-1221

Abstract

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.