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Nicolson Method (nicolson + method)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Solution to shape identification problem of unsteady heat-conduction fields

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2003
Eiji Katamine
Abstract This paper presents a numerical analysis method for shape determination problems of unsteady heat-conduction fields in which time histories of temperature distributions on prescribed subboundaries or time histories of gradient distributions of temperature in prescribed subdomains have prescribed distributions. The square error integrals between the actual distributions and the prescribed distributions on the prescribed subboundaries or in the prescribed subdomains during the specified period of time are used as objective functionals. Reshaping is accomplished by the traction method that was proposed as a solution to shape optimization problems of domains in which boundary value problems are defined. The shape gradient functions of these shape determination problems are derived theoretically using the Lagrange multiplier method and the formulation of material derivative. The time histories of temperature distributions are evaluated using the finite-element method for a space integral and the Crank,Nicolson method for a time integral. Numerical analyses of nozzle and coolant flow passage in a wing are demonstrated to confirm the validity of this method. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 212,226, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10086 [source]

Examination for adjoint boundary conditions in initial water elevation estimation problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010
T. KurahashiArticle first published online: 23 JUL 200
Abstract I present here a method of generating a distribution of initial water elevation by employing the adjoint equation and finite element methods. A shallow-water equation is employed to simulate flow behavior. The adjoint equation method is utilized to obtain a distribution of initial water elevation for the observed water elevation. The finite element method, using the stabilized bubble function element, is used for spatial discretization, and the Crank,Nicolson method is used for temporal discretizations. In addition to a method for optimally assimilating water elevation, a method is presented for determining adjoint boundary conditions. An examination using the observation data including noise data is also carried out. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Stability and accuracy of a semi-implicit Godunov scheme for mass transport

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004
Scott F. Bradford
Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Application of solid-phase concentration-dependent HSDM to the acid dye adsorption system

AICHE JOURNAL, Issue 1 2005
Vinci K. C. Lee
Abstract The fixed-bed adsorption of acid dyes onto granular activated carbon (Chemviron Filtrasorb 400) has been studied using a homogeneous surface diffusion model (HSDM). The model incorporates the external boundary layer mass transport and homogeneous diffusion inside the particle. A new orthogonal collocation method has been developed and used to solve the diffusion equations. This orthogonal collocation gives a faster solution method compared with the numerical Crank,Nicolson method. The surface diffusivity has been determined by an optimization procedure with minimization of sum of the error squared. The equilibrium relationship between the liquid-phase concentration and the solid-phase concentration has been described by the Redlich,Peterson isotherm. A solid-phase concentration-dependent surface diffusivity was introduced. The Darken model with the Redlich,Peterson isotherm was found to be a suitable correlation model for the adsorption of the acid dyes on carbon. The magnitude of the averaged Ds0 of each dye is in the order of AR114 > AB80 > AY117, which implies that, under the same solid-phase concentration gradient, the rate of mass transport diffusion is higher in AR114 than that in AB80 and AY117. This phenomenon may be explained by the different mobilities of the dye molecules present in the solution by the different arrangements of two sulfonic acid groups in the dye structures. © 2004 American Institute of Chemical Engineers AIChE J, 51: 323-332, 2005 [source]