P. C. Stegeman  M. E. Young  J. Soria  A. Ooi 《国际流体数值方法杂志》2013,71(7):805-829

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two‐dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

    

Yuan Li  Rong An 《国际流体数值方法杂志》2012,69(3):550-566

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

B. Nilsson  P. Hansbo 《国际流体数值方法杂志》2011,67(12):2015-2025

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

  总被引：1，自引：0，他引：1  

Yabin Sun  Piyamarn Sisomphon  Vladan Babovic  Eng Soon Chan 《国际流体数值方法杂志》2009,60(6):651-667

In recent years, a practice of tidal prediction based on a deterministic model or by a time series forecasting model has been established. A deterministic model can predict tidal movement and capture the dynamics of the flow pattern over the entire domain. However, due to the simplification of model settings and near shore effects, the accuracy of the numerical model can diminish. Time series forecasting is capable of capturing the underlying mechanism that may not be revealed in the deterministic model simulation. However, such data‐driven forecast fails to maintain accuracy with the progress of forecast horizon. In this paper, a scheme that combines the advantages of these two methods is introduced. The model errors are forecasted to different time horizons using a data‐driven approach, and are then superimposed on the simulation results in order to correct the model output. Based on the proposed method, it is found that the accuracy is significantly improved with more than 50% of the errors removed on the average. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

    

J. Hoffman 《国际流体数值方法杂志》2009,59(11):1241-1258

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c_D for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c_D to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10⁵ mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c_D. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

    

P. Benner  Z. Tomljanovi&#x;  N. Truhar 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2011,91(3):179-191

We consider a mathematical model of a linear vibrational system described by the second‐order differential equation , where M and K are positive definite matrices, called mass, and stiffness, respectively. We consider the case where the damping matrix D is positive semidefinite. The main problem considered in the paper is the construction of an efficient algorithm for calculating an optimal damping. As optimization criterion we use the minimization of the average total energy of the system which is equivalent to the minimization of the trace of the solution of the corresponding Lyapunov equation AX + X A^T = ‐I, where A is the matrix obtained from linearizing the second‐order differential equation. Finding the optimal D such that the trace of X is minimal is a very demanding problem, caused by the large number of trace calculations, which are required for bigger matrix dimensions. We propose a dimension reduction to accelerate the optimization process. We will present an approximation of the solution of the structured Lyapunov equation and a corresponding error bound for the approximation. Our algorithm for efficient approximation of the optimal damping is based on this approximation. Numerical results illustrate the effectiveness of our approach.  相似文献   

    

Michael Hinze  Fredi Trltzsch 《GAMM-Mitteilungen》2010,33(2):148-162

Solutions to optimization problems with pde constraints inherit special properties; the associated state solves the pde which in the optimization problem takes the role of a equality constraint, and this state together with the associated control solves an optimization problem, i.e. together with multipliers satisfies first and second order necessary optimality conditions. In this note we review the state of the art in designing discrete concepts for optimization problems with pde constraints with emphasis on structure conservation of solutions on the discrete level, and on error analysis for the discrete variables involved. As model problem for the state we consider an elliptic pde which is well understood from the analytical point of view. This allows to focus on structural aspects in discretization. We discuss the approaches First discretize, then optimize and First optimize, then discretize, and consider in detail two variants of the First discretize, then optimize approach, namely variational discretization, a discrete concept which avoids explicit discretization of the controls, and piecewise constant control approximations. We consider general constraints on the control, and also consider pointwise bounds on the state. We outline the basic ideas for providing optimal error analysis and complement our analytical findings with numerical examples which confirm our analytical results (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

    

Tal Ben‐Nun  Avi Ginsburg  Pablo Szkely  Uri Raviv 《Journal of Applied Crystallography》2010,43(6):1522-1531

X+ is a user‐friendly multi‐core accelerated program that fully analyses solution X‐ray scattering radially integrated images. This software is particularly useful for analysing supramolecular self‐assemblies, often found in biology, and for reconstructing the scattering signal in its entirety. The program enables various ways of subtracting background noise. The user selects a geometric model and defines as many layers of that shape as needed. The thickness and electron density of each layer are the fitting parameters. An initial guess is input by the user and the program calculates the form‐factor parameters that best fit the data. The polydispersity of one size parameter at a time can be taken into account. The program can then address the assembly of those shapes into different lattice symmetries. This is accounted for by fitting the parameters of the structure factor, using various peak line shapes. The models of the program and selected features are presented. Among them are the model‐fitting procedure, which includes both absolute and relative constraints, data smoothing, signal decomposition for separation of form and structure factors, goodness‐of‐fit verification procedures, error estimation, and automatic feature recognition in the data, such as correlation peaks and baseline. The program's intuitive graphical user interface runs on Windows PCs. Using X+, the exact structure of a microtubule in a crowded environment, and the structure, domain size, and elastic and interaction parameters of lipid bilayers, were obtained.  相似文献   

    

Eaton Lattman  David DeRosier 《Acta Crystallographica. Section A, Foundations and Advances》2008,64(2):341-344

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Ernesto Estevez‐Rams  Cristy Azanza‐Ricardo  Jorge Martínez García  Beatriz Aragn‐Fernndez 《Acta Crystallographica. Section A, Foundations and Advances》2005,61(2):201-208

A systematic use of binary codes derived from the Hägg symbol are used to study close‐packed polytypes. Seitz operators acting over the corresponding binary codes are defined and used. The number of non‐equivalent polytypes of a given length are calculated through the use of the Seitz operators. The same procedure is applied to the problem of counting the number of polytypes complying with a given symmetry group. All counting problems are reduced to an eigenvector problem in the binary code space. The symmetry of the binary codes leads to the different space groups to which polytypes can belong.  相似文献