Mehdi Dehghan  A. Pirkhedri 《国际流体数值方法杂志》2012,68(1):36-47

The MHD Falkner–Skan equation arises in the study of laminar boundary layers exhibiting similarity on the semi‐infinite domain. The proposed approach is equipped by the orthogonal Sinc functions that have perfect properties. This method solves the problem on the semi‐infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, the governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by the Sinc‐collocation method. It is shown that the Sinc‐collocation method converges to the solution at an exponential rate. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

    

Jeffrey C. Harris  Stéphan T. Grilli 《国际流体数值方法杂志》2012,68(12):1574-1604

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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   

    

Adrian Sescu  Abdollah A. Afjeh 《国际流体数值方法杂志》2011,67(11):1758-1768

Sonic boom focusing phenomenon can be predicted using the solution to the nonlinear Tricomi equation which is a hybrid (hyperbolic‐elliptic) second‐order partial differential equation. In this paper, the hyperbolic conservation law form is derived, which is valid in the entire domain. In this manner, the presence of two regions where the equation behaves differently (hyperbolic in the upper and elliptic in the lower half‐plane) is avoided. On the upper boundary, a new mixed boundary condition for the acoustic pressure is employed. The discretization is carried out using a discontinuous Galerkin (DG) method combined with a Runge–Kutta total‐variation diminishing scheme. The results show the accuracy of DG methods to solve problems involving sharp gradients and discontinuities. Comparisons with analytical results for the linear case, and other numerical results using classical explicit and compact finite difference schemes and weighted essentially non‐oscillatory schemes are included. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

    

H. Altenbach  I. Brigadnov  K. Naumenko 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2009,89(10):823-832

The rotation of an inertialess ellipsoidal particle in a shear flow of a Newtonian fluid has been firstly analyzed by Jeffery [17]. He found that the particle rotates such that the end of its axis of symmetry describes a closed periodic orbit. In the special case of a slender particle the Jeffery solution predicts the particle alignment parallel to the streamlines. In a recent publication [3] it was shown that the orbits are no longer observable if the rotary inertia is taken into account. Furthermore, in the case of a slender particle the inertia may cause the jump over the equilibrium alignment. In this paper we address a detailed analysis of the slender particle behavior in the shear flow. We recall the constitutive equation for the hydrodynamic moment and formulate equations of rotary motion. For a special initial condition we reduce the problem to a single second‐order ordinary differential equation with respect to the angle of rotation about a fixed axis. The phase portrait of this equation illustrates different cases of the particle behavior depending on the initial conditions and the “inertia” parameter. They include the particle alignment to a semi‐stable equilibrium position, the non‐uniform rotation about a fixed axis as well as the quantization effect (the particle locates in the neighborhood of the first equilibrium point over a relatively long time and then rotates towards the next equilibrium point).  相似文献   

    

K. Nakayama  T. Kakinuma 《国际流体数值方法杂志》2010,62(5):574-590

In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

    

L. P. Khoroshun  E. N. Shikula 《International Applied Mechanics》2005,41(4):345-351

The structural theory of short-term damage is generalized to particulate composites with nonlinearly elastic matrix and microdamageable inclusions. The basis for this generalization is the stochastic elasticity equations for a particulate composite with porous inclusions. Microvolumes of the material meet the Huber-Mises failure criterion. The damaged-microvolume balance equation and the equations relating macrostresses and macrostrains of a particulate composite with porous inclusions and physically nonlinear matrix constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for computing the microdamage-macrostrain relationships and deformation curves are proposed. Uniaxial tension curves are plotted for a particulate composite with linearly hardening matrix__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 3–11, April 2005.  相似文献   

    

J.‐J. Gervais  H. Sadiky 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2004,84(8):551-563

To compute solution paths of nonlinear systems F(x,λ) ≡ 0 depending upon a real parameter we propose a predictor‐corrector continuation method based on the third order Taylor polynomial or the (2,1)‐Padé approximation as predictor. The Taylor coefficients are computed using the exact expressions of the second and third orders derivatives of F. Our method works with any of the parametrizations: Pseudo‐arclength, local or secant length. A strategy for an adaptive steplength selection well suited for this high order predictor is derived which allows a good control of the accuracy with which the solution path is traced. Numerical examples demonstrate the efficiency of our method and give comparisons with previously proposed methods.  相似文献   

    

M. Foroughi  J. Struckmeier 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2004,84(7):499-504

We consider a simplified acoustic model to describe nonlinear phenomena occurring in loudspeakers. The first simplification is that we restrict to the one‐dimensional isentropic Euler equations in a slab, where on the right end a membrane is moving periodically with frequency ω and maximal displacement ϵ ≪ 1. Moreover we apply a perturbation method to the nonlinear model based on the small parameter ϵ, which yields linear hyperbolic first order systems coupled by nonlinear source terms of lower order. The asymptotic model is investigated numerically for two different frequencies ω.  相似文献   

    

Roger A. Sauer 《国际流体数值方法杂志》2014,75(7):519-545

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