Numerical solution of convection-diffusion problems at high Péclet number using boundary elements

Qiu, Zhimei; Wrobel, L.C.; Power, H.

doi:10.1002/(sici)1097-0207(19980315)41:5<899::aid-nme314>3.0.co;2-t

Cited by 40 publications

(24 citation statements)

References 14 publications

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“…Singh and Tanaka [19] reported studies of accuracy and efficiency of the boundary-element formulation for Peclet numbers as high as 100. Qiu et al [13] presented extremely good accuracy of the convective boundary elements for highly convective flows up to Pe ¼ 10 7 . Unfortunately, the numerical accuracy was investigated only at some preselected set of points in the computational domain, leaving the points with the sharpest concentration gradients out of consideration.…”

Section: Higher-order Bem For Convective Heat Diffusion 111mentioning

confidence: 99%

“…The numerical implementation proposed in [14] extended to viscous fluid flows at Reynolds numbers as high as 10 3 . More recently, Qiu et al [13] and Singh and Tanaka [18,19] presented semianalytical integration Figure 1. Surface plots of the steady-state g kernels for v 1 ¼ 1, v 2 ¼ 0, and…”

Section: Introductionmentioning

confidence: 96%

“…As an alternative to the well-established finite-difference, finite-volume, and finite-element methods, boundary-element methods (BEM) have been used extensively for steady-state linear convective transport phenomena in the past 15 years [6][7][8][9][10][11][12][13]. Initial developments using the conventional symmetric kernels, e.g., Laplace and Stokes fundamental solutions, demonstrated their applicability only for low and moderate Peclet numbers.…”

Section: Introductionmentioning

confidence: 99%

“…It is imperative that the convective nature of the phenomena enters the formulation through the kernels. The steady convective flow kernels have been successfully used for both linear [6][7][8][9][10]13] and nonlinear [11,[14][15][16][17] fluid flow problems at high Reynolds (or Peclet) numbers. We should emphasize that, due to the nature of the convective fundamental solutions, boundary-element formulations require no upwinding.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficiency and Accuracy of Higher-Order Boundary-Element Methods for Steady Convective Heat Diffusion

Grigoriev

Dargush

2004

Numerical Heat Transfer, Part B: Fundamentals

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Higher-order boundary-element methods (BEM) are presented for steady-state convective diffusion problems in two dimensions. The free-space steady convective diffusion fundamental solutions considered in this article provide an analytical upwinding for the entire Peclet number range, from zero to infinity. However, integration of the kernels over the boundary elements requires considerable attention, especially at higher Peclet numbers. We define an influence domain due to these convective kernels and then localize the surface integrations only within the domain of influence. The localization of the kernels becomes more prominent as the Peclet number of the flow increases. This, in turn, leads to increasing sparsity and improved conditioning of the global matrix. Consequently, iterative solvers become the primary choice. We consider an example problem with an exact solution, and investigate the accuracy and efficiency of the higher-order BEM formulations for Peclet numbers in the range from 200 to 200,000. The quartic boundary elements included in this study are shown to be extremely efficient.

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Section: Higher-order Bem For Convective Heat Diffusion 111mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficiency and Accuracy of Higher-Order Boundary-Element Methods for Steady Convective Heat Diffusion

Grigoriev

Dargush

2004

Numerical Heat Transfer, Part B: Fundamentals

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show abstract

“…In terms of the boundary element method by using the diffusion-convection fundamental solution, the problem can (at least for constant velocity field and constant coefficient) be described by pure boundary integral equations. This approach has been extensively studied in the past, where methods of solution have been proposed handling the problem up to very high Péclet numbers [1,2].…”

Section: Introductionmentioning

confidence: 99%

Solution of Energy Transport Equation with Variable Material Properties by BEM

Ravnik¹,

Škerget²,

Tibaut³

et al. 2017

Int. J. CMEM

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In this paper, we derive a boundary-domain integral formulation for the energy transport equation under the assumption that the fluid properties, through which the energy is transported by diffusion and convection, are spatially and temporally changing. The energy transport equation is a second-order partial differential equation of a diffusion-convection type, with the fluid temperature as the independent variable. The presented formulation does not require a calculation of the temperature gradient, thus it is, for a known fluid velocity field, linear.The final boundary-domain integral equation is discretized using a domain decomposition approach, where the equation is solved on each sub-domain, while subdomains are joined by compatibility conditions. The validity of the method is checked using several analytical examples. Convergence properties are studied yielding that the proposed discretization technique is second-order accurate.The developed method is used to simulate flow and heat transfer of nanofluids, which exhibit properties that depend on the solid particle concentration. A Lagrange-Euler approach is used.

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Efficiency of boundary element methods for time‐dependent convective heat diffusion at high Peclet numbers

Grigoriev

Dargush

2004

Commun. Numer. Meth. Engng.

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SUMMARYA higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192:4281-4298; 4299-4312; 4313-4335) for time-dependent convective heat di usion in two-dimensions appears to be a very attractive tool for e cient simulations of transient linear ows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. t 6 4Ä=V2 ) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and e ciency of BEM formulations for Peclet numbers in the range from 10 3 to 10 5 .

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Numerical solution of convection-diffusion problems at high Péclet number using boundary elements

Cited by 40 publications

References 14 publications

Efficiency and Accuracy of Higher-Order Boundary-Element Methods for Steady Convective Heat Diffusion

Efficiency and Accuracy of Higher-Order Boundary-Element Methods for Steady Convective Heat Diffusion

Solution of Energy Transport Equation with Variable Material Properties by BEM

Efficiency of boundary element methods for time‐dependent convective heat diffusion at high Peclet numbers

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