• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.161-165
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• 2004

In the vortex particle method based on the vorticity-velocity formulation for solving the Wavier-Stokes equations, the unsteady, incompressible, viscous laminar flow over a NACA 0012 foil is simulated. By applying an operator-splitting method, the 'convection' and 'diffusion' equations are solved sequentially at each time step. The convection equation is solved using the vortex particle method, and the diffusion equation using the particle strength exchange(PSE) scheme which is modified to avoid a spurious vorticity flux. The scheme is improved for variety body shape using one image layer scheme. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsively started NACA 0012 foil for Reynolds number 550.

• Korea-Australia Rheology Journal
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• v.18 no.2
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• pp.51-65
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• 2006

Of concern in the present theoretical investigation is the study of blood flow and convection-dominated diffusion processes in a model bifurcated artery under stenotic conditions. The geometry of the bifurcated arterial segment having constrictions in both the parent and its daughter arterial lumen frequently appearing in the diseased arteries causing malfunction of the cardiovascular system, is constructed mathematically with the introduction of suitable curvatures at the lateral junction and the flow divider. The streaming blood contained in the bifurcated artery is treated to be Newtonian. The flow dynamical analysis applies the two-dimensional unsteady incompressible nonlinear Wavier-Stokes equations for Newtonian fluid while the mass transport phenomenon is governed by the convection diffusion equation. The motion of the arterial wall and its effect on local fluid mechanics is, however, not ruled out from the present model. The main objective of this study is to demonstrate the effects of constricted flow characteristics and the wall motion on the wall shear stress, the concentration profile and on the mass transfer. The ultimate numerical solutions of the coupled flow and diffusion processes following a radial coordinate transformation are based on an appropriate finite difference technique which attain appreciable stability in both the flow phenomena and the convection-dominated diffusion processes.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1601-1606
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.7
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• pp.809-817
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.

• Journal of Wetlands Research
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• v.5 no.1
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• pp.67-78
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• 2003

The unsteady 2D convection and diffusion equation is solved numerically for the real-time simulation of suspended load propagation. The streamlined upwind scheme efficiently reduces numerical oscillations due to the high Peclet number in the convection dominant flow. By using the mixed boundary condition to express the external source terms or externally induced suspended load as a function of time in the algorithm, the model is capable of handling not only continuous load cases but also non-continuous suspended load influx. The suspended load transport modelwas verified using a case study for which an analytical exact solution is available and was applied to the real-time simulation of a suspended load influx case on the Mississippi River. The model algorithm can provide a framework upon which water quality as well as contaminant transport models can be built.