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 >

A.Kurenkov¹, A.Thess², H.Babovsky³

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 47-58, 2006, DOI:10.3970/fdmp.2006.002.047

Abstract A possibility for the determination of the interface between two electrically conducting fluids in cylindrical geometry is presented. The fluids with different conductivities are situated in an infinite cylinder. Along the axis of the cylinder a homogeneous electrical current is applied. The perturbation of the interface leads to an inhomogeneous electrical current and, therefore, results in an electrical potential change in the fluids and a magnetic field modification outside the fluids. The dependence of the electrical potential on the interface shape is obtained analytically. The interface profile is then recovered from data of the electrical More >

M.El-Gammal¹, J.M.Floryan¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 17-26, 2006, DOI:10.3970/fdmp.2006.002.017

Abstract Interface deformation and thermocapillary rupture in a cavity with free upper surface subject to concentrated heating from above is investigated. The dynamics of the process is modulated by placing different amounts of liquid in the cavity. The results determined for large Biot and zero Marangoni numbers show the existence of limit points beyond which steady, continuous interface cannot exist and processes leading to the interface rupture develop. Evolution of the limit point as a function of the mass of the liquid is investigated. The topology of the flow field is found to be qualitatively similar, More >

B.B. Karki¹, D. Bhattarai¹, L. Stixrude²

CMC-Computers, Materials & Continua, Vol.3, No.3, pp. 107-118, 2006, DOI:10.3970/cmc.2006.003.107

Abstract Computer modeling of liquid phase poses tremendous challenge: It requires a relatively large simulation size, long simulation time and accurate interatomic interaction and as such, it produces massive amounts of data. Recent advances in hardware and software have made it possible to accurately simulate the liquid phase. This paper reports the details of methodology used in the context of liquid simulations and subsequent analysis of the output data. For illustration purpose, we consider the results for the liquid phases of two geophysically relevant materials, namely MgO and MgSiO₃. The simulations are performed using the parallel first-principles More >

G.S. Palani¹, Nagesh R. Iyer¹, B. Dattaguru²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 107-120, 2005, DOI:10.3970/sdhm.2005.001.107

Abstract A posteriori error estimation and adaptive refinement technique for 2-D/3-D crack problems is the state-of-the-art. In this paper a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region has been proposed and used along with the stress based error estimator for reliable fracture analysis of 2-D crack problems. The proposed a posteriori error estimator is called the K-S error estimator. Further, h-adaptive mesh refinement strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance More >

J. Sladek¹, V. Sladek¹, J. Krivacek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 259-270, 2005, DOI:10.3970/cmes.2005.008.259

Abstract A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary More >

D.L. Young^1,2, J.W. Ruan²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 223-232, 2005, DOI:10.3970/cmes.2005.007.223

Abstract The applications of the method of fundamental solutions (MFS) for modeling the scattering of time-harmonic electromagnetic fields, which are governed by vector Helmholtz equations with coupled boundary conditions, are described. Various perfectly electric conductors are considered as the scatterers to investigate the accuracy of the numerical performance of the proposed procedure by comparing with the available analytical solutions. It is also the intention of this study to reveal the characteristics of the algorithms by comparisons with other numerical methods. The model is first validated to the exact solutions of the electromagnetic wave propagation problems for More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 149-172, 2005, DOI:10.3970/cmes.2005.007.149

Abstract The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some More >

Y.C. Hon¹, T. Wei²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 119-132, 2005, DOI:10.3970/cmes.2005.007.119

Abstract We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and More >

V. Sladek¹, J. Sladek¹, M. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 69-84, 2005, DOI:10.3970/cmes.2005.007.069

Abstract An efficient numerical method is proposed for 2-d potential problems in anisotropic media with continuously variable material coefficients. The method is based on the local integral equations (utilizing a fundamental solution) and meshfree approximation of field variable. A lot of numerical experiments are carried out in order to study the numerical stability, accuracy, convergence and efficiency of several approaches utilizing various interpolations. More >