• 제목/요약/키워드: unsteady diffusion convection equation

검색결과 6건 처리시간 0.018초

A Boundary Integral Equation Formulation for an Unsteady Anisotropic-Diffusion Convection Equation of Exponentially Variable Coefficients and Compressible Flow

  • Azis, Mohammad Ivan
    • Kyungpook Mathematical Journal
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    • 제62권3호
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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.

보오텍스 방법에 의한 순간 출발하는 2차원 날개 주위의 점성유동 모사 (Simulation of Viscous Flow Past NACA 0012 Poil using a Vortex Particle Method)

  • 이승재;김광수;서정천
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2004년도 춘계 학술대회논문집
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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.

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A mathematical model of blood flow and convective diffusion processes in constricted bifurcated arteries

  • Chakravarty S.;Sen S.
    • Korea-Australia Rheology Journal
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    • 제18권2호
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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.

입자와법에 의한 급 출발하는 타원형 실린더 주위 유동해석 (Numerical study of Flow around Impulsively Started Elliptic Cylinder using Vortex Particle Method)

  • 주남수;이상환
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2004년도 춘계학술대회
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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.

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입자와법에 의한 급 출발하는 타원형 실린더 주위 유동해석 (Numerical Study of Flow Around Impulsively Started Elliptic Cylinder Using Vortex Particle Method)

  • 이상환;주남수
    • 대한기계학회논문집B
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    • 제28권7호
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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.

Upwind Finite Element Model for Suspended Sediment Transport

  • 노준우
    • 한국습지학회지
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    • 제5권1호
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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.

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