Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Reservoir Simulation Based on the Finite Analytic Method

Abstract: Traditionally reservoir simulation has been accomplished by solution of reservoir flow models using variations of the methods of finite differences and less frequently by finite elements. The accuracy of these methods depends heavily on the size of grid blocks and time steps employed for the numerical solution. Consequently, computational time and memory requirements may be overwhelming in many cases. in the present study, a recently proposed method called the finite analytic method is shown to alleviate the difficulties associated with the conventional methods. The finite analytic method is operationally and principally different than the conventional finite difference and finite element methods in that a general analytical solution of the simulation model is used over mesh elements to obtain a numerical scheme. In this study, the methodology of formulating and calculating with this method is illustrated by means of a typical two-phase immiscible flow problem described by the Buckley-Leverett equation.

An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problems

Abstract: Our purpose is to establish a numerical method meeting the requirements of efficiency, stability, accuracy and easy-using Faced with these demands, in this paper, a hybrid method combining the advantages of 2 weak-form meshless methods is proposed for solving steady and transient heat conduction problems with temperature-dependent thermophysical properties in heterogeneous media In the process of the calculation for an arbitrary model discretized by the hybrid method, two different weak-form methods are used for the nodes categorized as: (1) boundary nodes, (2) near boundary interior nodes and (3) interior nodes A Galerkin free element method (GFREM) is proposed for the interior nodes of the Cartesian grid; and the local radial point interpolation method (LRPIM) is used for the other two types of nodes The GFREM using the Cartesian grid can greatly improve the accuracy and efficiency of the hybrid scheme Special decomposition technology to determine the irregular integral domain for LRPIM can increase the flexibility for complex models In addition, the full implicit finite difference scheme and Newton–Raphson method are used for solving transient nonlinear problems And non-crossing interface integral domain and support domain are employed for heterogeneous media Compared with other methods, numerical results show better accuracy, stability and efficiency from the numerical experiments

Analysis of antisymmetric cross-ply laminates using high-order shear deformation theories: a meshless approach

Abstract: For many years finite element method (FEM) was the chosen numerical method for the analysis of composite structures. However, in the last 20 years, the scientific community has witnessed the birth and development of several meshless methods, which are more flexible and equally accurate numerical methods. The meshless method used in this work is the natural neighbour radial point interpolation method (NNRPIM). In order to discretize the problem domain, the NNRPIM only requires an unstructured nodal distribution. Then, using the Voronoi mathematical concept, it enforces the nodal connectivity and constructs the background integration mesh. The NNRPIM shape functions are constructed using the radial point interpolation technique. In this work, the displacement field of composite laminated plates is defined by high-order shear deformation theories. In the end, several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature. The obtained results show the efficiency and accuracy of the NNRPIM formulation.