Delfim Soares Jr.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 341-360, 2015, DOI:10.3970/cmes.2015.105.341

Abstract In this work, a second-order time-marching procedure for dynamics is discussed, in which enhanced accuracy is enabled. The new technique is unconditionally stable (according to its parameter selection), it has no amplitude decay or overshooting, and it provides reduced period elongation errors. The method is based on displacement-velocity relations, requiring no computation of accelerations. It is efficient, simple and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the proposed technique. As it is described here, the new method has no drawbacks when compared to the Trapezoidal Rule (TR), which is one of… More >

G. P. Nikishkov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 335-361, 2013, DOI:10.3970/cmes.2013.093.335

Abstract Accuracy of the quarter-point and transition elements is investigated on one- and two-dimensional problems with inverse square-root singularity. It is demonstrated that most coefficients of the stiffness matrix of the quarter-point element are unbounded. However, numerical integration produces finite values of these coefficients. Influence of several parameters on the error in determining the stress intensity factor is studied. Solution accuracy can be improved using special distribution of element sizes and increasing the element integration order in the radial direction. More >

Deli Gao^1,2, Lianzhong Sun^1,3, Hongshu Wei⁴, Shunwen Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.2, pp. 143-162, 2012, DOI:10.3970/cmes.2012.089.143

Abstract Due to the complexity of forces acting on the down-hole tubular strings in extended reach drilling (ERD), the factors which influence the process should be taken into account as much as possible, in order to predict the down-hole drag & torque more accurately. This can help us to identify and prevent the problems related to downhole drag & torque in ERD. The effects of such factors, as the tubular buckling, the buoyancy, the mechanical resistance and the friction reducer, on down-hole drag & torque, are taken into account in this paper, in order to improve the accuracy of the prediction… More >

Taicong Chen¹, Haitao Ma¹, Wei Gao²

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 239-270, 2012, DOI:10.3970/cmes.2012.087.239

Abstract Monte Carlo simulation method has been used extensively in probabilistic analyses of engineering systems and its popularity has been growing. While it is widely accepted that the simulation results are asymptotically accurate when the number of samples increases, certain exceptions do exist. The major objectives of this study are to reveal the conditions of the applicability of Monte Carlo method and to provide new insights into the accuracy of the simulation results in stochastic structural analysis. Firstly, a simple problem of a spring with random axial stiffness subject to a deterministic tension is investigated, using normal and lognormal distributions. Analytical… More >

C.C. Tsai¹, Y.C. Lin², D.L. Young^2,3, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 103-114, 2006, DOI:10.3970/cmes.2006.016.103

Abstract In the applications of the method of fundamental solutions, locations of sources are treated either as variables or a priori known constants. In which, the former results in a nonlinear optimization problem and the other has to face the problem of locating sources. Theoretically, farther sources results in worse conditioning and better accuracy. In this paper, a practical procedure is provided to locate the sources for various time-independent operators, including Laplacian, Helmholtz operator, modified Helmholtz operator, and biharmonic operator. Wherein, the procedure is developed through systematic numerical experiments for relations among the accuracy, condition number, and source positions in different… More >

Gregory Baker¹, Huaijian Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 219-232, 2011, DOI:10.3970/cmes.2011.080.219

Abstract Boundary integral methods have proved very useful in the simulation of free surface motion, in part, because only information at the surface is necessary to track its motion. However, the velocity of the surface must be calculated quite accurately, and the error must be reasonably smooth, otherwise the surface buckles as numerical inaccuracies grow, leading to a failure in the simulation. For two-dimensional motion, the surface is just a curve and the boundary integrals are simple poles that may be removed, allowing spectrally accurate numerical integration. For three-dimensional motion, the singularity in the integrand, although weak, presents a greater challenge… More >

V. Sladek¹, J. Sladek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.3, pp. 243-264, 2010, DOI:10.3970/cmes.2010.063.243

Abstract The paper deals with diminishing the prolongation of the computational time due to procedural evaluation of the shape functions and their derivatives in weak formulations implemented with meshless approximations. The proposed numerical techniques are applied to problems of stationary heat conduction in functionally graded media. Besides the investigation of the computational efficiency also the accuracy and convergence study are performed in numerical tests. More >

Hao-Chueh Mai¹, Kuen-Hau Lin¹, Cheng-Hsiu Yang¹, Chao-An Lin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.1, pp. 45-62, 2010, DOI:10.3970/cmes.2010.061.045

Abstract A thermal BGK lattice Boltzmann model for flows with viscous heat dissipation is proposed. In this model, the temperature is solved by a separate thermal distribution function, where the equilibrium distribution function is similar to its hydrodynamic counterpart, except that the leading quantity is temperature. The viscous dissipation rate is obtained by computing the second-order moments of non-equilibrium distribution function, which avoids the discretization of the complex gradient term, and can be easily implemented. The proposed thermal lattice Boltzmann model is scrutinized by computing two-dimensional thermal Poiseuille flow, thermal Couette flow, natural convection in a square cavity, and three-dimensional thermal… More >

Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 147-176, 2009, DOI:10.3970/cmes.2009.041.147

Abstract Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This paper, therefore, extends the strategy proposed by [Aftosmis and Berger (2002)] to compute the refinement threshold. The extended strategy computes the refinement threshold based on a user desired number of grid cells and adaptations, thereby ensuring high computational efficiency. Because our main interest is flow around wind turbines, the adaptation strategy has been optimized for flow around wind turbine airfoils. The… More >

Hung-Chang Lee¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.041.001

Abstract The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They provide single-step explicit time integrators… More >