E. J. Sellountos¹, A. Sequeira¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.2, pp. 109-136, 2010, DOI:10.3970/cmes.2010.057.109

Abstract A new Local Boundary Integral Equation (LBIE) method is proposed for the solution of plane elastostatic problems. Non-uniformly distributed points taken from a Finite Element Method (FEM) mesh cover the analyzed domain and form background cells with more than four points each. The FEM mesh determines the position of the points without imposing any connectivity requirement. The key-point of the proposed methodology is that the support domain of each point is divided into parts according to the background cells. An efficient Radial Basis Functions (RBF) interpolation scheme is exploited for the representation of displacements in each cell. Tractions in the… More >

Y. T. Gu¹, P. Zhuang², F. Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.3, pp. 303-334, 2010, DOI:10.3970/cmes.2010.056.303

Abstract Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation(FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions… More >

Yu Miao¹, Qiao Wang¹, Bihai Liao^1,2, Junjie Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.053.001

Abstract As a truly meshless method, the Hybrid Boundary Node method (Hybrid BNM) does not require a `boundary element mesh', either for the purpose of interpolation of the solution variables or for the integration of `energy'. This paper presents a further development of the Hybrid BNM to the 2D elastodynamics. Based on the radial basis function (RBF) and the Hybrid BNM, it presents an inherently meshless, boundary-only technique, which named dual hybrid boundary node method (DHBNM), for solving 2D elastodynamics. In this study, the RBFs are employed to approximate the inhomogeneous terms via dual reciprocity method (DRM), while the general solution… More >

G. Kosec¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 191-216, 2009, DOI:10.3970/cmes.2009.047.191

Abstract This paper explores an application of a novel mesh-free Local Radial Basis Function Collocation Method (LRBFCM) [Sarler and Vertnik (2006)] in solution of coupled heat transfer and fluid flow problems with solid-liquid phase change. The melting/freezing of a pure substance is solved in primitive variables on a fixed grid with convection suppression, proportional to the amount of the solid fraction. The involved temperature, velocity and pressure fields are represented on overlapping sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The… More >

Sirajul Haq^1,2, Siraj-Ul-Islam³, Marjan Uddin^1,4

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 >

R. Vertnik¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 65-96, 2009, DOI:10.3970/cmes.2009.044.065

Abstract The application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of incompressible turbulent flow is explored in this paper. The turbulent flow equations are described by the low - Re number k-emodel with Jones and Launder [Jones and Launder (1971)] closure coefficients. The involved velocity, pressure, turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The velocity, turbulent kinetic energy and dissipation equations are solved through… More >

L.M.J.S. Dinis¹, R.M. Natal Jorge², J. Belinha³

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 1-34, 2009, DOI:10.3970/cmes.2009.044.001

Abstract The Natural Neighbour Radial Point Interpolation Method (NNRPIM) is extended to the large deformation analysis of non-linear elastic structures. The nodal connectivity in the NNRPIM is enforced using the Natural Neighbour concept. After the Voronoï diagram construction of the unstructured nodal mesh, which discretize the problem domain, small cells are created, the "influence-cells". These cells are in fact influence-domains entirely nodal dependent. The Delaunay triangles are used to create a node-depending background mesh used in the numerical integration of the NNRPIM interpolation functions. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed with the Radial Point Interpolators.… More >

Sirajul Haq¹, Siraj-ul-Islam², Arshed Ali³

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 1-24, 2008, DOI:10.3970/cmes.2008.038.001

Abstract In this paper we propose a meshfree technique for the numerical solution of the modified equal width wave (MEW) equation. Combination of collocation method using the radial basis functions (RBFs) with first order accurate forward difference approximation is employed for obtaining meshfree solution of the problem. Different types of RBFs are used for this purpose. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the results obtained from the existing methods. Propagation of a solitary wave, interaction of two… More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 157-188, 2008, DOI:10.3970/cmes.2008.031.157

Abstract This paper presents a new meshless numerical approach to solving a special class of moving interface problems known as the passive transport where an ambient flow characterized by its velocity field causes the interfaces to move and deform without any influences back on the flow. In the present approach, the moving interface is captured by the level set method at all time as the zero contour of a smooth function known as the level set function whereas one of the two new meshless schemes, namely the SL-IRBFN based on the semi-Lagrangian method and the Taylor-IRBFN scheme based on Taylor series… More >

M. Haji Mohammadi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.2, pp. 75-94, 2008, DOI:10.3970/cmes.2008.029.075

Abstract In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of steady incompressible flows, governed by the Navier--Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based on only a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction equation (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Radial basis functions (RBF) interpolation is employed in shape function… More >