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Nicholson Scheme (nicholson + scheme)

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Engineering100%

Selected Abstracts

A mixed finite element solver for liquid,liquid impacts

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004
Enrico Bertolazzi
Abstract The impact of a liquid column on a liquid surface initially at rest is numerically modelled to describe air entrapment and bubble formation processes. The global quantities of interest are evaluated in the framework of the potential theory. The numerical method couples a potential flow solver based on a Mixed Finite Element Method with an Ordinary Differential Equation solver discretized by the Crank,Nicholson scheme. The capability of the method in solving liquid,liquid impacts is illustrated in two numerical experiments taken from literature and a good agreement with the literature data is obtained. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A numerical approach for groundwater flow in unsaturated porous media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006
F. Quintana
Abstract In this article, a computational tool to simulate groundwater flow in variably saturated non-deformable fractured porous media is presented, which includes a conceptual model to obtain analytical expressions of water retention and hydraulic conductivity curves for fractured hard rocks and a numerical algorithm to solve the Richards equation. To calculate effective saturation and relative hydraulic conductivity curves we adopt the Brooks,Corey model assuming fractal laws for both aperture and number of fractures. A standard Galerkin formulation was employed to solve the Richards' equation together with a Crank,Nicholson scheme with Richardson extrapolation for the time discretization. The main contribution of this paper is to group an analytical model of the authors with a robust numerical algorithm designed to solve adequately the highly non-linear Richards' equation generating a tool for porous media engineering. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A Crank,Nicholson-based unconditionally stable time-domain algorithm for 2D and 3D problems

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2007
Xin Xie
Abstract It has been shown that both ADI-FDTD and CN-FDTD are unconditionally stable. While the ADI is a second-order approximation, CN is only in the first order. However, analytical expressions reveal that the CN-FDTD has much smaller truncation errors and is more accurate than the ADI-FDTD. Nonetheless, it is more difficult to implement the CN than the ADI, especially for 3D problems. In this paper, we present an unconditionally stable time-domain method, CNRG-TD, which is based upon the Crank,Nicholson scheme and implemented with the Ritz,Galerkin procedure. We provide a physically meaningful stability proof, without resorting to tedious symbolic derivations. Numerical examples of the new method demonstrate high precision and high efficiency. In a 2D capacitance problem, we have enlarged the time step, ,t, 400 times of the CFL limit, yet preserved good accuracy. In the 3D antenna case, we use the time step, ,t, 7.6 times larger that that of the ADI-FDTD i.e., more than 38 times of the CFL limit, with excellent agreement of the benchmark solution. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 261,265, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22101 [source]

On the modified Crank,Nicholson difference schemes for parabolic equation with non-smooth data arising in biomechanics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2010
Allaberen Ashyralyev
Abstract In the present paper, we consider the mixed problem for one-dimensional parabolic equation with non-smooth data generated by the blood flow through glycocalyx on the endothelial cells. Stable numerical method is developed and solved by using the r-modified Crank,Nicholson schemes. Numerical analysis is given for a constructed problem. Copyright © 2008 John Wiley & Sons, Ltd. [source]