Abstract
In this paper, we consider the stationary double-diffusive natural convection model, which can model heat and mass transfer phenomena. Based on the fixed point theorem, the existence and uniqueness of the considered model are proved. Moreover, we design three finite element iterative methods for the considered problem. Under the uniqueness condition of a weak solution, iterative method I is stable. Compared with iterative method I, iterative method II is stable with a stronger condition. Moreover, iterative method III is stable with the strongest condition. From the perspective of viscosity, iterative method I displays well in the case of a low viscosity number, iterative method II runs well with slightly low viscosity, and iterative method III can deal with high viscosity. Finally, some numerical experiments are presented for testing the correctness of the theoretic analysis.
Highlights
The double-diffusive natural convection model, which does incorporate the velocity vector field as well as the pressure field, and contains the temperature field and the concentration field, has been widely used in scientific, engineering and industrial applications such as nuclear design, cooling of electronic equipment, aircraft cabins, insulation with double pane windows, and so on
The impact of nanofluid on free convection heat transfer was investigated by researchers in [4]
In [16], the curvature-based stabilization method was considered for double-diffusive natural convection flows in the presence of a magnetic field and unconditionally stable and optimally accurate second order approximations were obtained
Summary
The double-diffusive natural convection model, which does incorporate the velocity vector field as well as the pressure field, and contains the temperature field and the concentration field, has been widely used in scientific, engineering and industrial applications such as nuclear design, cooling of electronic equipment, aircraft cabins, insulation with double pane windows, and so on. A projection-based stabilized finite element method for steady-state natural convection problem was considered in [8]. In [16], the curvature-based stabilization method was considered for double-diffusive natural convection flows in the presence of a magnetic field and unconditionally stable and optimally accurate second order approximations were obtained. Some iterative finite element methods for steady Navier–Stokes equations with different viscosities were discussed in [19]. Huang et al [23] have considered and analyzed the Oseen, Newton and Stokes iterative methods for the 2D steady Navier–Stokes equations He et al [24]. The main work in this paper is to design, analyze, and compare three iteration methods to solve nonlinear equations based on the finite element discretization.
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