A combined method for solving 2D incompressible flow and heat transfer by spectral collocation method and artificial compressibility method

Zhang, Jingkui; Dong, Honggang; Zhou, Enze; Li, Ben-Wen; Tian, Xi-Yan

doi:10.1016/j.ijheatmasstransfer.2017.04.051

Cited by 23 publications

(10 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Batina et al (2014) studied the melting of a phase change material inside a two-dimensional cavity numerically by a high-accuracy numerical approximation based on the SCMs. There are also many other works (Akrish et al , 2019; Nambiar et al , 2019; Pourjafar et al , 2018; Zhang et al , 2017; Sun et al , 2015; Yokota and Barba, 2013) that verified the characteristics of spectral methods. Just because of the good performance, the spectral methods are used widely for fluid flow and heat transfer.…”

Section: Introductionmentioning

confidence: 84%

See 1 more Smart Citation

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Zhang

Cui

et al. 2020

HFF

Self Cite

View full text Add to dashboard Cite

Purpose The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer. Design/methodology/approach The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method. Findings The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step. Research limitations/implications It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer. Practical implications The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes. Originality/value The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

show abstract

Section: Introductionmentioning

confidence: 84%

“…The SCM is one kind of spectral methods. It also has the characteristics of global approximations, exponential convergence and high accuracy as demonstrated in those works (Jiang and Li, 2018; Pourjafar et al , 2018; Zhang et al , 2017; Ellahi et al , 2016; Sun et al , 2015; Batina et al , 2014).…”

Section: Introductionmentioning

confidence: 88%

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Zhang

Cui

et al. 2020

HFF

Self Cite

View full text Add to dashboard Cite

show abstract

“…The trigonometric solution (28) in their paper has the same mathematical structure as our solution in (38) with = = 1 and = −1, = 1. Solutions (29), (32), and (33) in their article can be equivalently transformed to our solution in (38) by choosing = 0, = 1 and = 1, = 0. Finally, rational solutions (36) and (37) in their paper with of degree two in the denominators are structurally equivalent to our rational solution in (40).…”

Section: Whenmentioning

confidence: 99%

“…Examples of the methods for obtaining analytical approximate solutions to NPDEs are the variational iteration method [22,23] (VIM), the Adomian decomposition method [24,25] (ADM), the homotopy perturbation method [26,27] (HPM), and the reduced differential transform method [28]. In addition, the examples of useful methods for solving NPDEs numerically are the generalized finite difference method [29], the finite volume method [30], the finite element method [31], the spectral collocation method [32], and the Galerkin finite element method [33]. However, we prefer, if possible, to obtain exact solutions of NPDEs.…”

Section: Introductionmentioning

confidence: 99%

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2
Sirisubtawee
¹
,
Koonprasert
²

2018
Advances in Mathematical Physics
44
0
19
0
View full text Add to dashboard Cite

We apply the ( / 2 )-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

show abstract

“…In the penalty method, the errors in the divergence of velocity are transferred to the boundaries [24]. An alternative related technique is the artificial compressibility technique (ACT) [25][26][27][28][29], in which the deviations from incompressibility determine ∂p/∂t rather than p itself. Also, the ACT diffuses errors in velocity divergence.…”

Section: Introductionmentioning

confidence: 99%

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

Mousa

Ali

2021

Journal of Taibah University for Science

View full text Add to dashboard Cite

A new combined technique is developed for studying free convection of magnetohydrodynamic unsteady incompressible flow in a square cavity that partially heated from lower wall and regular cooling from lateral walls. Convection has been studied for several lengths of heat source, Hartman and the Rayleigh numbers. The local and average Nusselt numbers are calculated and presented graphically along the heat source portion. The proposed technique is a combination of the method of lines (MOL) and a developed penalty-artificial compressibility technique (PACT). Unsteady penalty compressibility governing equations are used instead of solving steady-state balances. The penalty and artificial compressibility factors are estimated using a deduced stability restriction. The validation of the MOL-PACT is verified by comparing the current data with other numerical and experimental ones existing in the literature. The proposed technique provides a new choice through the investigation of MHD mass and heat transfer.

show abstract

A combined method for solving 2D incompressible flow and heat transfer by spectral collocation method and artificial compressibility method

Cited by 23 publications

References 33 publications

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2
Sirisubtawee
¹
,
Koonprasert
²

2018
Advances in Mathematical Physics
44
0
19
0
View full text Add to dashboard Cite

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

Contact Info

Product

Resources

About

A combined method for solving 2D incompressible flow and heat transfer by spectral collocation method and artificial compressibility method

Cited by 23 publications

References 33 publications

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Performance of combined spectral collocation method and artificial compressibility method for 3D incompressible fluid flow and heat transfer

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2Sirisubtawee1, Koonprasert2 2018Advances in Mathematical Physics440190View full textAdd to dashboardCite

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

Contact Info

Product

Resources

About

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2
Sirisubtawee
¹
,
Koonprasert
²

2018
Advances in Mathematical Physics
44
0
19
0
View full text Add to dashboard Cite