R.L. Taylor

Bio: R.L. Taylor is an academic researcher from Polytechnic University of Catalonia. The author has contributed to research in topics: Regularized meshless method & Fluid mechanics. The author has an hindex of 2, co-authored 2 publications receiving 1126 citations.

A finite point method in computational mechanics. applications to convective transport and fluid flow

Abstract: The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non-self adjoint equations typical of convective-diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.

A stabilized finite point method for analysis of fluid mechanics problems

Abstract: In this paper a meshless procedure termed ‘the finite point method’ for solving convection-diffusion and fluid flow type problems is presented. The method is based on the use of a weighted least-square interpolation procedure together with point collocation for evaluating the approximation integrals. Special emphasis is given to the stabilization of the convective terms and the Neumann boundary condition which has been found to be essential to obtain accurate results. Some examples of application to diffusive and convective transport and compressible flow problems using quadratic FP interpolations are presented.

Meshless methods: An overview and recent developments

Abstract: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.

Review: Meshless methods: A review and computer implementation aspects

Abstract: The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enrichment, point collocation methods, several boundary condition enforcement schemes and corresponding test cases. Several one and two-dimensional examples in elastostatics are given including weak and strong discontinuities and testing different ways of enforcing essential boundary conditions.

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

Abstract: The purpose of this review paper is to present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics. Such modelling is essential for studying the fundamental processes occurring in rocks and for rock engineering design. The review begins by explaining the special nature of rock masses and the consequential difficulties when attempting to model their inherent characteristics of discontinuousness, anisotropy, inhomogeneity and inelasticity. The rock engineering design backdrop to the review is also presented. The different types of numerical models are outlined in Section 2, together with a discussion on how to obtain the necessary parameters for the models. There is also discussion on the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations. In Section 3, the largest section, states-of-the-art and advances associated with the main methods are presented in detail. In many cases, for the model to adequately represent the rock reality, it is necessary to incorporate couplings between the thermal, hydraulic and mechanical processes. The physical processes and the equations characterizing the coupled behaviour are included in Section 4, with an illustrative example and discussion on the likely future development of coupled models. Finally, in Section 5, the advances and outstanding issues in the subject are listed and in Section 6 there are specific recommendations concerning quality control, enhancing confidence in the models, and the potential future developments.

A point interpolation meshless method based on radial basis functions

Abstract: A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis. This non-singularity is useful in constructing well-performed shape functions. Furthermore, the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least-squares approximation. In addition, the partial derivatives of shape functions are easily obtained, thus improving computational efficiency. Examples on curve/surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high. Copyright © 2002 John Wiley & Sons, Ltd.

Meshfree and particle methods and their applications

Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#