• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.233-245
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• 2003

A time fractional advection-dispersion equation is Obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order ${\alpha}$(0 < ${\alpha}$ $\leq$ 1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional advection-dispersion equation.

• Journal of Soil and Groundwater Environment
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• v.8 no.3
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• pp.8-12
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• 2003

The centrifuge test result on capped sediment was compared to the advection- dispersion equation proposed for one layered to predict contaminant transport parameters. The fitted contaminant transport parameters for the centrifuge test results were one to three orders of magnitude greater than the estimated parameters from the advection-dispersion equation. This indicates that the centrifuge model over estimated the contaminant transport phenomena. Thus, the centrifuge provides a non-conservative approach to modeling contaminant transport. It should be also noted that the advection-dispersion equation used in this study is a one layered model. Two layered modeling approaches are more appropriate for modeling this data since there are two layers with different partitioning coefficients. Further research is required to model the centrifuge test using two-layered advection-dispersion models.

• Journal of computational fluids engineering
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• v.9 no.3
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• pp.8-17
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• 2004

A Semi-Lagrangian method based on CIP(Cubic Interpolated Pseudoparticle)method is proposed and it is applied to solve the two dimensional advection equation. Especially the attentions are given to settle the pole problem and to enhance the accuracy in solving the advection equation on the spherical coordinate system. Tn this algorithm, the CU method is employed as the Semi-Lagrangian method and extended to the spherical coordinate system. To enhance the accuracy of the solution, the spatial discretization is made by CIP method. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional rotating cosine bell problem and the frontogenesis problem are simulated by the present scheme. As results, it is confirmed that the present scheme gives an accurate solution and settles the pole problem in the advection equation on the sphere.

• 한국방재학회:학술대회논문집
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• 2007.02a
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• pp.177-180
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• 2007

Numerical simulations on the suspended load in the Do jang fish port are carried out. Suspended load is analysed by using the two-dimensional advection-diffusion equation. To describe behaviors of a pollutant in costal zone, a split-operator method is applied to the numerical model. The advection part is first solved by SOWMAC and then the diffusion part is solved by a three-level locally implicit scheme.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Journal of Environmental Science International
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• v.11 no.9
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Korean Journal of Hydrosciences
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• v.6
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.7
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• pp.871-878
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• 2004

An accurate adaptive mesh refinement based on the CIP method is proposed and it is applied to solve the two dimensional advection equations. In this method, the level set function is employed to refine and merge the computation cells. To enhance the accuracy of the solution, the spatial discretization is made by the CIP method. The CIP method has many advantages such as the third order accuracy, less diffusivity, and shape conserving. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy, and capability of the proposed algorithim, two dimensional rotating slotted cylinder and idealized frontogenesis are numerically simulated by the present scheme. As results, it is confirmed that the present method gives an efficient, reasonable solution in the advection equation.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.22-27
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• 2006

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third-order QUICKEST explicit finite difference schemes respectively to solve the pure advection equation in order to prevent the occurrence of numerical oscillations. Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes are applied to experimental data for simulating the 2D mixing in a straight trapezoidal channel to test the model capability. Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.

• Water Engineering Research
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• v.4 no.1
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• pp.45-58
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• 2003

Two-dimensional depth-averaged advection-dispersion equation was simulated using FEM. In the straight rectangular channel, the advection-dispersion processes are simulated so that these results can be compared with analyti-cal solutions for the transverse line injection and the point injection. In the straight domain the standard Galerkin method with the linear basis function is found to be inadequate to the advection-dispersion analysis compared to the upwind finite element scheme. The experimental data in the S-curved channel were compared with the result by the numerical model using SUPG(Streamline upwind Petrov-Galerkin) method.