J.T. Zhou¹, Q.W. Ma^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.2, pp. 179-210, 2010, DOI:10.3970/cmes.2010.056.179

Abstract In this paper, the Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) is further developed to model 3D breaking waves. For this purpose, the technique for identifying free surface particles called Mixed Particle Number Density and Auxiliary Function Method (MPAM) and the semi-analytical technique for estimating the domain integrals for 2D cases are extended to 3D cases. In addition, a new semi-analytical technique is developed to deal with the local spherical surface integrals. The numerical results obtained by the newly developed method will be compared with experimental data available in literature and satisfactory agreement will be shown. More >

Claire Heaney^1,2, Charles Augarde², Andrew Deeks²

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.2, pp. 153-178, 2010, DOI:10.3970/cmes.2010.056.153

Abstract Meshless methods continue to generate strong interest as alternatives to conventional finite element methods. One major area of application as yet relatively unexplored with meshless methods is elasto-plasticity. In this paper we extend a novel numerical method, based on the Meshless Local Petrov-Galerkin (MLPG) method, to the modelling of elasto-plastic materials. The extended method is particularly suitable for problems in geomechanics, as it permits inclusion of infinite boundaries, and is demonstrated here on footing problems. The current usage of meshless methods for problems involving plasticity is reviewed and guidance is provided in the choice of various modelling parameters. More >

R. Martin¹, D. Komatitsch^1,2, S. D. Gedney³, E. Bruthiaux^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 17-42, 2010, DOI:10.3970/cmes.2010.056.017

Abstract Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a second-order finite-difference time scheme. However it is often of interest to increase the order of the time-stepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simulations. We study how to define and implement a new unsplit non-convolutional PML called the Auxiliary Differential Equation PML (ADE-PML), based on a high-order Runge-Kutta time-stepping scheme and optimized at grazing incidence. We demonstrate that when a second-order time-stepping… More >

J. Sladek¹, V. Sladek¹, M. Wünsche², Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 223-252, 2009, DOI:10.3970/cmes.2009.054.223

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve the interface crack problem between two dissimilar anisotropic elastic solids. Both stationary and transient mechanical and thermal loads are considered for two-dimensional (2-D) problems in this paper. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variations of the displacements and temperature are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, one obtains… More >

R. Avila¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 15-64, 2009, DOI:10.3970/cmes.2009.054.015

Abstract The Meshless Local Petrov Galerkin (MLPG) method is used to solve the non-steady two dimensional Navier-Stokes equations. Transient laminar flow field calculations have been carried out in domains wherein certain surfaces have: (i) a sliding motion, (ii) a harmonic motion, (iii) an undulatory movement, and (iv) a contraction-expansion movement. The weak form of the governing equations has been formulated in a Cartesian coordinate system and taking into account the primitive variables of the flow field. A fully implicit pressure correction approach, which requires at each time step an iterative process to solve in a sequential manner the equations which govern… More >

Luca Bergamaschi^1,2, ,Ángeles Martínez², Giorgio Pini²

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.3, pp. 191-216, 2009, DOI:10.3970/cmes.2009.049.191

Abstract A meshless model, based on the Meshless Local Petrov-Galerkin (MLPG) approach, is developed and implemented in parallel for the solution of axi-symmetric poroelastic problems. The parallel code is based on a concurrent construction of the stiffness matrix by the processors and on a parallel preconditioned iterative method of Krylov type for the solution of the resulting linear system. The performance of the code is investigated on a realistic application concerning the prediction of land subsidence above a deep compacting reservoir. The overall code is shown to obtain a very high parallel efficiency (larger than 78% for the solution phase) and… More >

K. Han¹, Y. T. Feng¹, D. R. J. Owen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.2, pp. 143-162, 2009, DOI:10.3970/cmes.2009.049.143

Abstract Motivated by Hottel's crossed-string method, this paper presents an accurate algorithm for the evaluation of the geometric view factors in a randomly packed bed of circular particles of various sizes. The radiative heat exchange can thus be predicted accurately. The solution procedure is illustrated and the solution accuracy is assessed via a numerical example. More >

J. Sladek¹, V. Sladek¹, P. Solek², C.L. Tan³, Ch. Zhang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 61-96, 2009, DOI:10.3970/cmes.2009.047.061

Abstract The meshless local Petrov-Galerkin (MLPG) method for transient linear thermoelastic analysis is presented. Orthotropic material properties are considered here. In uncoupled thermoelasticity, the temperature field is not influenced by displacements. Therefore, in the first step, the heat conduction equation is solved for the temperature distribution in the domain. The equations of motion are then solved with the inertial term considered. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two- and three-dimensional problems. Local integral equations are written on small sub-domains with circular or spherical shapes. They surround nodal… More >

Q.W. Ma^1,2, J.T. Zhou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 277-304, 2009, DOI:10.3970/cmes.2009.043.277

Abstract Following our previous work, the Meshless Local Petrov-Galerin me -thod based on Rankine source solution (MLPG_R) will be extended in this paper to deal with breaking waves. For this purpose, the governing equation for pressure is improved and a new technique called Mixed Particle Number Density and Auxiliary Function Method (MPAM) is suggested for identifying the free surface particles. Due to complexity of the problem, two dimensional (2D) breaking waves are only concerned here. Various cases are investigated and some numerical results are compared with experimental data available in literature to show the newly developed method is robust. More >

J. Sladek¹, V. Sladek¹, P. Solek²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 223-252, 2009, DOI:10.3970/cmes.2009.043.223

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical… More >