• East Asian mathematical journal
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• v.40 no.1
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• pp.109-118
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• 2024

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection-diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection-diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.599-609
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• 2014

We refer to the saturation assumptions on the finite element approximation for a one dimensional convection-diffusion model. By examining piecewise linear finite elements with refined mesh by half and hierarchical bases, we verify the saturation results, respectively.

• Fisheries and Aquatic Sciences
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• v.7 no.2
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• pp.90-95
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• 2004

An analytical model for predicting the convection-diffusion of solute dumped in a homogeneous open sea of constant water depth has been developed in a time-integral form. The model incorporates spatially uniform, uni-directional, mean and oscillatory currents for horizontal convection, the settling velocity for the vertical convection, and the anisotropic turbulent diffusion. Two transformations were introduced to reduce the convection-diffusion equation to the Fickian type diffusion equation, and then the Galerkin method was then applied via the expansion of eigenfunctions over the water column derived from the Sturm-Liouville problem. A series of calculations has been performed to demonstrate the applicability of the model.

• Journal of Electrochemical Science and Technology
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• v.13 no.3
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• pp.347-353
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• 2022

Agarose hydrogel, a solid electrolyte, was investigated voltammetrically in terms of transport properties and natural convection effects using a ferrocenyl compound as a redox probe. To confirm the diffusion properties of solute on the agarose interface, the diffusion coefficients (D) of ferrocenemethanol in agarose hydrogel were determined by cyclic voltammetry (CV) according to the concentration of agarose hydrogel. While the value of D on the agarose interface is smaller than that in the bulk solution, the square root of the scan rate-dependent peak current reveals that the mass transport behavior of the solute on the agarose surface shows negligible convection or migration effects. In order to confirm the reduced natural convection on the gel interface, scan rate-dependent CV was performed in the solution phase and on the agarose surface, respectively. Slow scan voltammetry at the gel interface can determine a conventional and reproducible diffusion-controlled current down to a scan rate of 0.3 mV/s without any complicated equipment.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.14 no.4
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• pp.160-168
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• 2004

We investigate the effects of solutal convection on the crystal growth rate in a horizontal configuration for diffusive-convection conditions and purely diffusion conditions achievable in a low gravity environment for a nonlinear thermal gradient. It is concluded that the solutally-driven convection due to the disparity in the molecular weights of the component A $(Hg_2Br_2)$ and B (CO) is stronger than thermally-driven convection for both the nonlinear and the linear thermal profiles, corresponding to $Gr_t= 8.5{\times}10^3,\; Gr_s = 1.05{\times}10^5$. For both solutal and thermal convection processes, the growth rates for the linear thermal profile (conducting walls) are greater than for the nonlinear case. With the temperature humps, there are found to be observed in undersaturation for diffusive-convection processes ranging from $D_{AB}$ = 0.087 to 0.87. For the vertical configurations, the diffusion mode is so much dominated that the growth rate and interfacial distribution is nearly regardless of the gravitational accelerations. Also, the diffusion mode is predominant over the convection for the gravity levels less than 0.1 $g_0$ for the horizontally oriented configuration.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.1-20
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• 2006

This paper presents the interior penalty discontinuous Galerkin finite element methods (DGFEM) for solving the rotating disk electrode problems in electrochemistry. We present results for the simple E reaction mechanism (convection-diffusion equations), the EC' reaction mechanism (reaction-convection-diffusion equation) and the ECE and $EC_2E$ reaction mechanisms (linear and nonlinear systems of reaction-convection-diffusion equations, respectively). All problems will be in one dimension.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.83-100
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• 2010

In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid V-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.

• 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.

• Bulletin of the Korean Chemical Society
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• v.32 no.6
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• pp.1970-1974
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• 2011

The effects of convection on the measurement of the diffusion coefficients of liquids by the pulsed gradient spin echo (PGSE) NMR method at low temperature are discussed. To examine the generation of convective flows, we used four different types of sample tubes in the diffusion measurements with temperature variation; a normal 5 mm NMR tube, a Shigemi tube, an ELISE type tube, and a capillary tube. Below room temperature, the calculated diffusion coefficients of chloroform in 5 mm o.d. type tubes increased with decreasing temperature, while those in the capillary tube decreased linearly. The convective flow was found to be significant even at low temperature and it seemed to be mainly induced by the transverse temperature gradient. It was also found that the capillary tube was most appropriate to measure the diffusion coefficients, since its small diameter is effective in suppressing the convective flows at both high and low temperatures.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.