Home / Journals / CMES / Vol.12, No.1, 2006
Table of Content
  • Open Access

    ARTICLE

    On Three-dimensional Effects in Propagation of Surface-breaking Cracks

    A. Dimitrov1, F.-G. Buchholz2, E. Schnack3
    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 1-26, 2006, DOI:10.3970/cmes.2006.012.001
    Abstract Crack propagation in 3D-structures cannot be reduced (in general) to a series of plane problems along the crack front edge, due to the existence of some "corners'' on the crack front, where the elastic fields are of a real three-dimensional nature. The most important example for such a corner ist the point, where the crack front intersects a free surface of the body. According to the concept of weak and strong singularities, it is possible to obtain the asymptotics for the stress intensity factor (SIF) as well as the strain energy release rate (SERR) in the neighborhood of such a… More >

  • Open Access

    ARTICLE

    The Method of External Sources (MES) for Eigenvalue Problems with Helmholtz Equation

    S.Yu. Reutskiy1
    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 27-40, 2006, DOI:10.3970/cmes.2006.012.027
    Abstract In this paper a new boundary method for eigenproblems with the Helmholtz equation in simply and multiply connected domains is presented. The solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with the differential operator studied. The method shows a high precision in simply and multiply connected domains and does not generate spurious eigenvalues. The results of the numerical experiments justifying the method are presented. More >

  • Open Access

    ARTICLE

    A Time Adaptive Scheme for the Solution of the Advection Equation in the Presence of a Transient Flow Velocity

    A. P. S. Selvadurai1, Wenjun Dong
    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 41-54, 2006, DOI:10.3970/cmes.2006.012.041
    Abstract A Fourier analysis conducted on both the spatial and the temporal discretizations of the governing partial differential equation shows that the Courant number as well as the time marching scheme have significant influences on the numerical behaviour of a Modified Least Squares (MLS) method for the solution of the advection equation. The variations of the amplification factor and the relative phase velocity with the Courant number and the dimensionless wave number indicate that when Courant number is equal to unity, the MLS method with the specified time-weighting and upwind function gives accurate results. This conclusion is confirmed by the numerical… More >

  • Open Access

    ARTICLE

    An Efficient Backward Group Preserving Scheme for the Backward in Time Burgers Equation

    Chein-Shan Liu1
    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 55-66, 2006, DOI:10.3970/cmes.2006.012.055
    Abstract In this paper we are concerned with the numerical integration of Burgers equation backward in time. We construct a one-step backward group preserving scheme (BGPS) for the semi-discretization of Burgers equation. The one-step BGPS is very effectively to calculate the solution at an initial time t = 0 from a given final data at t = T, which with a time stepsize equal to T and with a suitable grid length produces a highly accurate solution never seen before. Under noisy final data the BGPS is also robust to against the disturbance. When the solution appears steep gradient, several steps… More >

  • Open Access

    ARTICLE

    Past Cone Dynamics and Backward Group Preserving Schemes for Backward Heat Conduction Problems

    C.-S. Liu1, C.-W. Chang2, J.-R. Chang2
    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067
    Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X˙ = B(X,t)X with t ∈ R, X ∈ Mn+1 lying on the past cone and Bso(n,1), was derived for the backward differential equations system x· =f(x,t), t ∈ R, x ∈ Rn. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step… More >

Share Link

WeChat scan