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Derivative Term (derivative + term)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Development of a class of multiple time-stepping schemes for convection,diffusion equations in two dimensions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006
R. K. Lin
Abstract In this paper we present a class of semi-discretization finite difference schemes for solving the transient convection,diffusion equation in two dimensions. The distinct feature of these scheme developments is to transform the unsteady convection,diffusion (CD) equation to the inhomogeneous steady convection,diffusion-reaction (CDR) equation after using different time-stepping schemes for the time derivative term. For the sake of saving memory, the alternating direction implicit scheme of Peaceman and Rachford is employed so that all calculations can be carried out within the one-dimensional framework. For the sake of increasing accuracy, the exact solution for the one-dimensional CDR equation is employed in the development of each scheme. Therefore, the numerical error is attributed primarily to the temporal approximation for the one-dimensional problem. Development of the proposed time-stepping schemes is rooted in the Taylor series expansion. All higher-order time derivatives are replaced with spatial derivatives through use of the model differential equation under investigation. Spatial derivatives with orders higher than two are not taken into account for retaining the linear production term in the convection,diffusion-reaction differential system. The proposed schemes with second, third and fourth temporal accuracy orders have been theoretically explored by conducting Fourier and dispersion analyses and numerically validated by solving three test problems with analytic solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Improved PI controller with delayed or filtered integral mode

AICHE JOURNAL, Issue 12 2002
Jietae Lee
Integral action is almost always included in process control systems to eliminate steady-state offset without uncertain process gain. The open-loop pole, however, at the origin of the integral term causes some problems such as integral windup. Various methods to solve these problems were studied. For better control performance and robustness, a filter was added to the integral term, which decouples the effective frequency ranges between the integral and proportional terms without degradation of the integral action. It produces a phase lead in a certain frequency range without having a derivative term, enhancing the control performances and stability robustness. Based on the internal model control method or the direct synthesis method, tuning rules for the proposed controller are given. [source]

ADI-FDTD method perturbed by the second order cross derivative terms

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 7 2008
Ki-Bok Kong
Abstract A two-step FDTD method as a compromise of conditional stability and reduced splitting error is formulated and its numerical stability is investigated. It is the perturbed form to the ADI-FDTD method by the addition of second order cross derivative term. It is validated from the comparison of numerical anisotropy and numerical error over the ADI-FDTD that numerical performances can be improved by controlling the perturbed term within the stable region of the cross derivative term. © Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1822,1826, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23479 [source]

Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2001
R. K. Mohanty
Abstract In 1996, Mohanty et al. [1] presented a fourth-order finite difference solution of a two space dimensional nonlinear hyperbolic equation with Dirichlet boundary conditions. In 1998, Mohanty et al. [2] discussed a fourth-order approximation at first time level for the numerical solution of the one space dimensional hyperbolic equation. In both the cases, they have discussed the stability analysis for the linear hyperbolic equation having first-order space derivative terms. Recently, Mohanty et al. [3] have developed fourth-order difference formulas for the three space dimensional quasi-linear hyperbolic equations and obtained fourth-order approximation at first time level. In this article, we extend our strategy for solving the two space dimensional quasi-linear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed. Linear stability analysis and fourth-order approximation at first time level for the two space dimensional quasi-linear hyperbolic equation are also discussed. The results of the numerical experiments are compared with the exact solution. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 607,618, 2001 [source]