The characteristic variational multiscale method for time dependent conduction–convection problems

Wu, Jilian; GUI, Dongwei; Liu, Demin; Feng, Xinlong

doi:10.1016/j.icheatmasstransfer.2015.08.020

Cited by 16 publications

(12 citation statements)

References 16 publications

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“…We present the isotherms, streamlines and isobars in Figure 11 with increasing Ra = 1, 10 4 and 10 5 . We can see that, for cases Ra = 1,10 4 , the isotherms, streamlines and isobars computed by our method simulate the temperature field, fluid field, and pressure field very well, which also conforms with the numerical results presented by Su et al (2014) and Wu et al (2015). Notes: (a) The decoupled characteristic stabilized FEM with P 1 -P 1 -P 1 triples; (b) the decoupled characteristic stabilized FEM with P 1 -P 0 -P 1 triples; (c) the standard characteristic FEM with P 1 b-P 1 -P 1 triples; (d) P 1 -P 1 -P 1 triples without addition of a stabilization term Stabilized finite element method Furthermore, our method still exhibited good stability behavior even with higher Rayleigh number Ra = 10 5 .…”

Section: Methodssupporting

confidence: 87%

Characteristic stabilized finite element method for non-stationary conduction-convection problems

Wang

Mahbub

Zheng

2019

HFF

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Purpose This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems. Design/methodology/approach To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P1-P1-P1 and P1-P0-P1 triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw. Findings The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates. Originality/value Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.

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Section: Methodssupporting

confidence: 87%

Characteristic stabilized finite element method for non-stationary conduction-convection problems

Wang

Mahbub

Zheng

2019

HFF

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“…The characteristic methods are proven to be efficient in many physical problems, especially for convection-dominated problems (Qian et al , 2014). Wu et al (2015a) formulated the characteristic variational multiscale (C-VMS) finite element method (FEM) for time dependent conduction-convection problem. In this paper, we use the char- acteristic method combining variational multiscale strategy to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional FEMs.…”

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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“…The coarse scale is then projected into an appropriate subspace while the fine scale is directly stabilized against highly localized affects such as those seen in turbulence modeling. This method has been further developed in later work and applied to problems involving incompressible flows [21,22,23] and convection-diffusion [24,25,26].…”

Section: Multiple Concurrent Methods Have Been Developed For Couplingmentioning

confidence: 99%

An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications

Lin

Smith

Liu

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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A concurrent multiscale method is developed to model time-dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved. Ensuring this energetic consistency among scales enables the implementation of high fidelity physics-based models at critical locations within the coarse-scale to temporally and spatially resolve highly complex and localized phenomena. To achieve this, only Neumann boundary conditions are applied over the fine scale domain, ensuring a conservative formulation. The coarse-scale solution is used to reconstruct these Neumann boundary conditions on the fine scale, which are then used to evolve a separate system of governing equations. The results on the fine scale are then sent back to the coarse scale through an energy-based homogenization scheme. Transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness, including the coupling of a phase field model at the fine scale to a coarse-scale heat equation.

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The characteristic variational multiscale method for time dependent conduction–convection problems

Cited by 16 publications

References 16 publications

Characteristic stabilized finite element method for non-stationary conduction-convection problems

Characteristic stabilized finite element method for non-stationary conduction-convection problems

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

An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications

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