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• Open Access

ARTICLE

Numerical Solution of Nonlinear Schrodinger Equations by Collocation Method Using Radial Basis Functions

Sirajul Haq1,2, Siraj-Ul-Islam3, Marjan Uddin1,4
CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 115-136, 2009, DOI:10.3970/cmes.2009.044.115
Abstract A mesh free method for the numerical solution of the nonlinear Schrodinger (NLS) and coupled nonlinear Schrodinger (CNLS) equation is implemented. The presented method uses a set of scattered nodes within the problem domain as well as on the boundaries of the domain along with approximating functions known as radial basis functions (RBFs). The set of scattered nodes do not form a mesh, means that no information of relationship between the nodes is needed. Error norms L2, L are used to estimate accuracy of the method. Stability analysis of the method is given to demonstrate its practical applicability. More >

• Open Access

ARTICLE

Consistent Boundary Conditions for 2D and 3D Lattice Boltzmann Simulations

Chih-Fung Ho1, Cheng Chang1, Kuen-Hau Lin1, Chao-An Lin1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 137-156, 2009, DOI:10.3970/cmes.2009.044.137
Abstract Consistent formulations of 2D and 3D pressure and velocity boundary conditions along both the stationary and non-stationary plane wall and corner for lattice Boltzmann simulations are proposed. The unknown distribution functions are made function of local known distribution functions and correctors, where the correctors at the boundary nodes are obtained directly from the definitions of density and momentum. This boundary condition can be easily implemented on the wall and corner boundary using the same formulation. Discrete macroscopic equation is also derived for steady fully developed channel flow to assess the effect of the boundary condition on the solutions, where the… More >

• Open Access

ARTICLE

Numerical Modelling of Electromagnetic Waves by Explicit Multi-Level Time-Step FEM-BEM Coupling Procedures

Delfim Soares Jr.1
CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 157-176, 2009, DOI:10.3970/cmes.2009.044.157
Abstract The numerical modelling of electromagnetic waves by finite element - boundary element coupling procedures is discussed here, taking into account time-domain approaches. In this study, the global model is divided into different sub-domains and each sub-domain is analysed independently and explicitly at each time-step of the analysis: the interaction between the different sub-domains of the global model is accomplished by interface procedures. A multi-level time-step algorithm is considered in order to improve the flexibility, accuracy and stability (especially when conditionally stable time-marching procedures are employed) of the coupled analysis. At the end of the paper, numerical examples are presented, illustrating… More >

• Open Access

ARTICLE

Numerical Solution of 2D Natural Convection in a Concentric Annulus with Solid-Liquid Phase Change

R. Avila1, F.J. Solorio1
CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 177-202, 2009, DOI:10.3970/cmes.2009.044.177
Abstract Heat transfer processes involving phase change either, solidification or melting, appear frequently in nature and in industrial applications. In this paper the convective patterns that arise from a 2D shear driven annular flow (without and with melting), are presented. The convective annular flow with radial gravity can be considered as a simplified model of the atmospheric flow in the terrestrial equatorial plane (bounded by the warm surface of the Earth and the cold tropopause). The governing equations have been numerically solved by the Spectral Element Method. The numerical results reported in this paper, for the cases without melting (at two… More >

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