Browsing by Author "Huang, LH"

Now showing 1 - 6 of 6

An accurate integral-based scheme for advection-diffusion equation
(2001-10-01)
Tsai, TL
;
Yang, JC
;
Huang, LH
;
土木工程學系
;
Department of Civil Engineering
This paper proposes an accurate integral-based scheme for solving the advection-diffusion equation. In the proposed scheme the advection-diffusion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary points of adjacent elements. The proposed scheme is unconditionally stable and results in a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the proposed scheme can be extended straightforwardly from one-dimensional to multi-dimensional problems without much difficulty and complication. To investigate the computational performances of the proposed scheme five numerical examples are considered: (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow; (ii) one-dimensional viscous Burgers equation; (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow; (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow; and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, the fully time-centred implicit QUICK scheme and the fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, the ADI-TCSD scheme and the MOSQUITO scheme for two-dimensional problems, the proposed scheme shows convincing computational performances. Copyright (C) 2001 John Wiley & Sons, Ltd.
An accurate integral-based scheme for dispersion equation
(2001)
Tsai, TL
;
Yang, JC
;
Huang, LH
;
土木工程學系
;
Department of Civil Engineering
This paper proposes an accurate integral-based scheme for solving dispersion equation. In the newly-proposed scheme the dispersion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary point of adjacent elements. The newly-proposed scheme is unconditionally stable and preserves a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the newly-proposed scheme, originally developed for one-dimensional problems, can be extended straightforward to multi-dimensional problems. To investigate the computational performances of the newly-proposed scheme five numerical examples are considered : (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow, (ii)one-dimensional viscous burger's equation, (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow, (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, fully time-centred implicit QUICK scheme and fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, ADI-TCSD scheme and MOSQUITO scheme for two-dimensional problems, the newly-proposed scheme shows convincing computational performances.
Body force effect on consolidation of porous elastic media due to pumping
(2006-01-01)
Tsai, TL
;
Chang, KC
;
Huang, LH
;
防災與水環境研究中心
;
Disaster Prevention and Water Environment Research Center
In this study, the linear poro-elasticity theory is applied to examine the body force effect on consolidation of porous media due to pumping. The steady-state solutions of displacement and incremental effective stress for a stratum of clay sandwiched between sandy strata are analytically given. The effect of body force could be represented by the body force number that depends on Lame's constants, porosity, and the thickness of porous media. The consolidation of clay is significantly related not only to the body force number but also to the ratio of water table depression in upper and lower sandy strata due to pumping. The neglect of body force will severely underestimate the displacement and incremental effective stress when porous media are soft or thick, or both. This might lead to potential flaws in engineering practice, such as the calculation of soil settlement.
Characteristics method using cubic-spline interpolation for advection-diffusion equation
(2004-06-01)
Tsai, TL
;
Yang, JC
;
Huang, LH
;
土木工程學系
;
防災與水環境研究中心
The characteristics method by using the cubic-spline interpolation is comparable to the Holly-Preissmann scheme in solving the advection portion of the advection-diffusion equation. In order to conduct a cubic-spline interpolation, an additional constraint must be specified at each endpoint. In general, four types of endpoint constraints are available, i.e., the first derivative, second derivative, quadratic, and not-a-knot constraints. The goal of this paper is to examine each type of endpoint constraints. Two hypothetical cases are used to conduct the investigation. Among the four types of constraints examined herein, the not-a-knot constraint and the first derivative constraint with high-order finite difference approximation yield the best results. However, as far as accuracy and simple implementation are concerned the not-a-knot constraint should be the best choice in solving the advection-diffusion equation.
Groundwater modeling by layer based three-dimensional concept
(2000)
Tsai, TL
;
Huang, LH
;
Yang, JC
;
土木工程學系
;
Department of Civil Engineering
Due to its simplicity and efficiency, the conventional quasi three-dimensional concept has been widely applied in analyzing groundwater flow in multiaquifer system, especially for regional problem. But the conventional quasi three-dimensional concept is not able to deal with the discontinuous and interconnected strata and fully three-dimensional flow. Therefore, in order not only to overcome these shortcomings but also to maintain efficiency, we propose a new layer based three-dimensional concept to develop a groundwater simulation model. This new concept assumes that the pore pressure of every aquifer and aquitard in the vertical direction can be depicted by the quadratic polynomial interpolation function, then the vertical integration is performed on each layer to ensure the continuity of pore pressure and flux at the interfaces between any two layers. The finite analytical numerical method is adopted to develop the present groundwater simulation model. The results show that the present model is capable of simulating fully three-dimensional flow pattern.
Hybrid finite-difference scheme for solving the dispersion equation
(2002-01-01)
Tsai, TL
;
Yang, JC
;
Huang, LH
;
土木工程學系
;
Department of Civil Engineering
An efficient hybrid finite-difference scheme capable of solving the dispersion equation with general Peclet conditions is proposed. In other words, the scheme can simultaneously deal with pure advection, pure diffusion, and/or dispersion. The proposed scheme linearly combines the Crank-Nicholson second-order central difference scheme and the Crank-Nicholson Galerkin finite-element method with linear basis functions. Using the method of fractional steps, the proposed scheme can be extended straightforwardly from one-dimensional to multidimensional problems without much difficulty. It is found that the proposed scheme produces the best results, in terms of numerical damping and oscillation, among several non-split-operator schemes. In addition, the accuracy of the proposed scheme is comparable with a well-known and accurate split-operator approach in which the Holly-Preissmann scheme is used to solve the pure advection process while the Crank-Nicholson second-order central difference scheme is applied to the pure diffusion process. Since the proposed scheme is a non-split-operator approach, it does not compute the two processes separately. Therefore, it is simpler and more efficient than the split-operator approach.