Implicit–explicit schemes of finite element method for the non-stationary thermal convection problems with temperature-dependent coefficients

Zhang, Tong; Feng, Xinlong; Yuan, Jinyun

doi:10.1016/j.icheatmasstransfer.2016.06.011

Cited by 15 publications

(2 citation statements)

References 14 publications

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“…For natural convection problem, which has a wide range of applications in many research fields (Wu et al , 2017b, 2016), the density difference in the fluid occurring due to temperature gradient is the driving mechanism of fluid motion[1]. In case that the density variation is small, it can be modeled by using a Boussinesq approximation, which treats the density as a constant but with an added buoyancy force, and most literature studies the constant density natural convection based on the Boussinesq approximation (Boland and Layton, 1990; Du et al , 2015; Feng et al , 2011; Huang et al , 2015, 2013, 2012; Liao, 2012, 2010; Si et al , 2014; Szumbarski et al , 2014; Su et al , 2017a, 2017b, 2014a, 2014b; Sun et al , 2011; Davis, 1983; Wang et al , 2018a, 2018b; Wu et al , 2015b, 2017a, 2016; Zhang et al , 2016, 2018]). However, in most geophysical flows and many other situations, fluid motion is usually driven by large temperature differences, which results in a considerable density change and the Boussinesq approximation is no longer valid.…”

Section: Introductionmentioning

confidence: 99%

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

Wang

Feng

2019

HFF

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Purpose The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem. Design/methodology/approach The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P2, P2, P1, P2) to approximate the density, velocity, pressure and temperature field. Findings The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well. Originality/value Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

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Section: Introductionmentioning

confidence: 99%

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

Wang

Feng

2019

HFF

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“…Owing to the various flow and heat transfer problems have been proposed by natural convection problem. Many researchers have studied these equations (Du et al , 2014; Feng et al , 2012; Feng et al , 2011; He and Zhang, 2015; Huang et al , 2015; Su et al , 2016a; Su et al , 2016b; Wu et al , 2015a; Zhu et al , 2017; Zhang et al , 2016). For these methods of solving natural convection problems, we only choose some of them to describe.…”

Section: Introductionmentioning

confidence: 99%

Parallel two-step finite element algorithm based on fully overlapping domain decomposition for the time-dependent natural convection problem

Ping

Zhao

et al. 2019

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Purpose This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem. Design/methodology/approach The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P1b-P1-P1) and solve a linear approximation based on a higher-order element pair (P2-P1-P2) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Findings Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Originality/value The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

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Scheme for Evolutionary Navier-Stokes-Fourier System with Temperature Dependent Material Properties Based on Spectral/hp Elements

Pech

2020

Lecture Notes in Computational Science and Engineering

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The computational algorithm for evolutionary Navier-Stokes-Fourier system with temperature dependent material properties (density, viscosity and thermal conductivity) is presented and tested. As a consequence of the thermal expansion, the velocity field is not divergence free. The system fully couples the momentum balance with non-linear advection-diffusion equation for temperature. The model is suitable for low speed flow simulations of the Newtonian, calorically perfect fluid, which obeys Fourier law. The algorithm is an extension of a well known semi-implicit scheme for incompressible Navier-Stokes equations in primitive variable formulation. Performance is tested on manufactured solution, what gives an overview to the temporal convergence. Comparison with experimental data is also presented.

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Implicit–explicit schemes of finite element method for the non-stationary thermal convection problems with temperature-dependent coefficients

Cited by 15 publications

References 14 publications

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

Parallel two-step finite element algorithm based on fully overlapping domain decomposition for the time-dependent natural convection problem

Scheme for Evolutionary Navier-Stokes-Fourier System with Temperature Dependent Material Properties Based on Spectral/hp Elements

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