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  • 1
    Electronic Resource
    Electronic Resource
    Boundary layer flow on a long thin cylinder (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 628-637 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The development of the boundary layer along a long thin cylinder aligned with the flow is considered. Numerical solutions are presented and compared with previous asymptotic results. Very near the leading edge the flow is given by the Blasius solution for a flat plate. However, there is soon a significant deviation from Blasius flow, with a thinner boundary layer and higher wall shear stress. Linear normal mode stability of the flow is investigated. It is found that for Reynolds numbers less than a critical value of 1060 the flow is unconditionally stable. Also, axisymmetric modes are only the fourth least stable modes for this problem, with the first three three-dimensional modes all having a lower critical Reynolds number. Further, for Reynolds numbers above the critical value, the flow is unstable only for a finite distance, and returns to stability sufficiently far downstream. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1427921
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  • 2
    Electronic Resource
    Electronic Resource
    Influences of random disturbances on simultaneous resonances of nonlinear coupling systems (1988)
    Springer
    Acta mechanica solida Sinica 1 (1988), S. 181-193 
    Details
    ISSN: 0894-9166
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The influences of random disturbances on simultaneous resonances of nonlinear coupling systems are dealt with in this paper. First, the approximate probability distribution of behavior of nonlinear system is presented through using the stochastic averaging method. Secondly, using the Monte Carlo numerical simulation method, we study the above mentioned system. Both conclusions are nearly same. It is confirmed that the stochastic averaging method is one of efficient methods for dealing with nonlinear random vibration problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02208141
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Time dependent periodic Navier-Stokes flows on a two-dimensional torus (1996)
    Springer
    Communications in mathematical physics 179 (1996), S. 577-597 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The dynamical behaviour of an incompressible viscous fluid flow on a two-dimensional torus externally excited by a spatially periodic force is investigated. The flow field, described by Navier-Stokes equations, is found to possess a sequence of time-periodic solutions which bifurcate from a single steady state solution (i.e. Hopf bifurcations). This result is based on a combination of analysis and computations, and each provides corroborative evidence to the findings of the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02100098
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Long-time behavior of Navier-Stokes flow on a two-dimensional torus excited by an external sinusoidal force (1997)
    Springer
    Journal of statistical physics 86 (1997), S. 301-335 
    Details
    ISSN: 1572-9613
    Keywords: Navier-Stokes equations ; bifurcations ; dynamical systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we study the Navier-Stokes flow on the two-dimensional torusS 1 ×S 1 excited by the external force (k 2 sinky, 0) and find the long-time behavior for the flow starting from some states, whereS 1=[0,2π](mod 2π). Especially for the casek=2, it follows from an analysis and computation that the Navier-Stokes flow with the initial state cos(mx+ny) or sin(mx+ny) will likely evolve through at most one step bifurcation to either a steady-state solution or a time-dependent periodic solution for any Reynolds number and integersm andn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02180208
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  • 5
    Electronic Resource
    Electronic Resource
    Renormalization calculations of immiscible flow (1993)
    Springer
    Transport in porous media 12 (1993), S. 237-260 
    Details
    ISSN: 1573-1634
    Keywords: Effective properties ; relative permeability ; pseudoization ; rescaling ; heterogeneity ; simulation ; reservoir characterization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Oil reservoir properties can vary over a wide range of length scales. Reservoir simulation of the fluid flow uses numerical grid blocks have typical lengths of hundreds of metres. We need to specify meaningful values to put into reservoir engineering calculations given the large number of heterogeneities that they have to encompass. This process of rescaling data results in the calculation of ‘effective’ or ‘pseudo’ rock properties. That is a property for use on the large scale incorporating the many heterogeneities measured on smaller scales. For single phase flow, a variety of techniques have been tried in the past. These range from very simple statistical estimates to detailed numerical simulation. Unfortunately, the simple estimates tend to be inaccurate in real applications and the numerical simulation can be computationally expensive if not impossible for very fine grid representations of the reservoir. Likewise, pseudorelative permeabilities are time consuming to generate and often inaccurate. Real-space renormalization is an alternative technique which has been found to be computationally efficient and accurate when applied to single-phase flow. This approach solves the problem regionally rather than trying to solve the whole problem in one simulation. The effective properties of small regions are first calculated and then placed on a coarse grid. The grid is further coarsened and the process repeated until a single effective property has been calculated. This has enabled calculation of effective permeability of extremely large grids to be performed, up to 540 million grid blocks in one application. This paper extends the renormalization technique to two-phase fluid flow and shows that the method is at least 100 times faster than conventional pseudoization techniques. We compare the results with high resolution numerical simulation and conventional pseudoization methods for three different permeability models. We show that renormalization is as accurate as the conventional methods when used to predict oil recovery from heterogeneous systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00624460
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  • 6
    Electronic Resource
    Electronic Resource
    Computational methods for some non-linear wave equations (1999)
    Springer
    Journal of engineering mathematics 35 (1999), S. 323-338 
    Details
    ISSN: 1573-2703
    Keywords: computational methods ; KP/GKP equation ; solitary waves ; stability analysis ; phase error.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Computational methods based on a linearized implicit scheme and a predictor-corrector method are proposed for the solution of the Kadomtsev–Petviashvili (KP) equation and its generalized from (GKP). The methods developed for the KP equation are applied with minor modifications to the generalized case. An inportant advantage to be gained from the use of the linearized implicit method over the predictor-corrector method which is conditionally stable, is the ability to vary the mesh length, and thereby reducing the computational time. The methods are analysed with respect to stability criteria. Numerical results portraying a single line-soliton solution and the interaction of two-line solitons are reported for the KP equation. Moreover, a lump-like soliton (a solitary wave which decays to zero in all space dimensions) and the interaction of two lump solitons are reported for the KP equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004464217776
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  • 7
    Electronic Resource
    Electronic Resource
    Numerical solutions of a damped Sine-Gordon equation in two space variables (1995)
    Springer
    Journal of engineering mathematics 29 (1995), S. 347-369 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Numerical solutions of the perturbed Sine-Gordon equation in two space variables, arising from a Josephson junction are presented. The method proposed arises from a two-step, one parameter method for the numerical solution of second-order ordinary differential equations. Though implicit in nature, the method is applied explicitly. Global extrapolation in both space and time is used to improve the accuracy. The method is analysed with respect to stability criteria and numerical dispersion. Numerical results are obtained for various cases involving line and ring solitons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00042761
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  • 8
    Electronic Resource
    Electronic Resource
    A linearized implicit pseudo-spectral method for certain non-linear water wave equations (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 977-993 
    Details
    ISSN: 1069-8299
    Keywords: third-order KdV equation ; fifth-order KdV equation ; pseudo-spectral ; implicit method ; unconditional stability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the third- and fifth-order Korteweg-de Vries equations and their generalizations. The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time.An important advantage to be gained from the use of this method over the pseudo-spectral scheme proposed by Fornberg and Whitham (a Fourier transform treatment of the space variable together with a leap-frog scheme in time) which is conditionally stable, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable.The method presented here is for the Korteweg-de Vries equations and their generalized forms, but it can be implemented to a broad class of non-linear wave equations (equation (1)), with obvious changes in the various formulae.To illustrate the application of this method, numerical results portraying a single soliton solution and the collision of two solitons are reported for the third- and fifth-order Korteweg-de Vries equations. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Hydrodynamic confficients of some heaving cylinders of arbitrary shape (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 13 (1978), S. 17-33 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fluid forces acting on a uniform cylinder with an infinitely long axis, heaving in the free surface or an infinite ideal fluid, are described in terms of its ‘added mass’ and ‘damping coefficient’. The techniques of multipole expansion and multiparameter conformal transformation are adopted for such calculations and applied to shapes which cannot be adequately represented by the conventional, and more rudimentary, ‘Lewis form fit’. The shapes referred to are both relevant to ship bows, one being a ‘fine section’ and the other a ‘bulbous section’. The parameters which influence the accuracy of the solution are examined. Results for these two sections are computed and compared with results based on (a) the ‘Lewis form approximation’ and (b) the ‘Frank's close fit method’ which employs a singularity representation.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620130103
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  • 10
    Electronic Resource
    Electronic Resource
    A second-order, chaos-free, explicit method for the numerical solution of a cubic reaction problem in neurophysiology (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 213-224 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A second order explicit method is developed for the numerical solution of the initialvalue problem w′(t) ≡ dw(t)/dt = φ(w), t 〉 0, w(0) = W0, in which the function φ(w) = αw(1 - w) (w - a), with α and a real parameters, is the reaction term in a mathematical model of the conduction of electrical impulses along a nerve axon. The method is based on four first-order methods that appeared in an earlier paper by Twizell, Wang, and Price [Proc. R. Soc. (London) A 430, 541-576 (1990)]. In addition to being chaos free and of higher order, the method is seen to converge to one of the correct steady-state solutions at w = 0 or w = 1 for any positive value of α. Convergence is monotonic or oscillatory depending on W0, α, a, and l, the parameter in the discretization of the independent variable t. The approach adopted is extended to obtain a numerical method that is second order in both space and time for solving the initial-value boundary-value problem ∂u/∂t = κ∂2u/∂x2 + αu(1 - u)(u - a) in which u = u(x,t). The numerical method so developed obtained the solution by solving a single linear algebraic system at each time step. © 1993 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090302
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