Meshfree methods

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

Comparison of Selected Meshless Methods for Analysis of Steady, Fully-Developed, Laminar Flow of an Incompressible Newtonian Fluid in Internally Finned Tubes

Abstract: Fluid flow in internally finned tubes is a very important problem from a practical point of view. In the literature there are many different numerical methods which were used for analysis this problem. However to the best knowledge of the authors of the present paper there are no so many papers in which meshless methods were applied for this purpose. The main advantages of these methods are: easy implementation, semi-analytical form of the approximate solution and no need for mesh generation. In the paper these meshless methods are compared in application for analysis of incompressible, fully-developed, Newtonian fluid flow in an internally finned tube.

Magnetic Field Analyses by Using Free Mesh Method and Their Visualization

Abstract: netron sputtering system. The numerical analyses by using the finite element method (FEM) are applied in various fields. In FEM, the pre-processing such as a mesh generation is a complicated procedure. Yagawa et al. introduced the free mesh method (FMM), which is a kind of the meshless methods. 1), 2) In the electromagnetic analysis, the FMM was applied in Refs. 3) and 4). In order to obtain more accurate solution efficiently in such problems, the distribution of nodes has to be dense in a region where the change of the potential distribution is large. It is necessary to distribute the nodes adaptively to examine the proper profiles of electromagnetic features. In this study, the magnetic field analysis is carried out in the magnetron sputtering system shown in Fig. 1. In order to solve the magnetic field accurately and efficiently, the distribution of nodes used in the FEM calculations should be changed adaptively due to the vector potential distribution or magnetic field configuration. The estimation of the values of the magnetic flux density is carried out in the FMM to get the distribution of nodes adaptively. The indicator is the difference of the value on the node from the average one inside the element. The adaptive subdivision of nodes is carried out by using this estimation. 5)

Orthotropic plate dynamics by a novel meshfree method

Abstract: Publisher Summary This chapter deals with a novel meshfree method for the dynamic analysis of orthotropic plates under the Kirchhoff small deflection theory. The approach starts from a modified function whose stationarity conditions lead to the meshfree plate dynamic model through a discretization process—based on the use of orthotropic plate static fundamental solutions. The resolving system obtained is characterized by—frequency independent stiffness and mass matrices, which preserve the symmetry and definiteness properties of the continuum. Moreover, these operators are computed by boundary integrals of regular kernels. The method allows the application of standard numerical routines available for finite element dynamic models.

Assessment Of Two Pressure-velocity CouplingStrategies For Local Meshless Numerical Method

Abstract: The performance of two pressure-velocity coupling strategies, associated with the primitive variable solution of incompressible Newtonian fluid with the meshless Local Radial Basis Function Collocation Method (LRBFCM), is compared with respect to computational efficiency, stability, accuracy and spatial convergence. The LRBFCM is structured with multiquadrics on five noded support domains. The explicit time stepping is used. The BackwardFacing Step problem (BFS) has been selected as a benchmark problem, previously tackled by several numerical methods. The semi-local fractional step method (FSM) and completely local pressure-velocity couplings (LPVC) are compared. The numerical results are validated against previously published data. The results are represented and compared in terms of a convergence plot of the reattachment position. We show that both approaches provide reasonable results; however, LVPC is less computationally complex and less stable in comparison to FSM.

Plenary lecture 6: a weakened weak (W2) formulation for certified solutions with bounds, real-time computation and inverse analysis of biomechanics problems

Abstract: This paper introduces first a weakened weakform (W2) using a generalized gradient smoothing technique for an unified formulation of a wide class of compatible and incompatible displacement methods including settings of the finite element methods (FEM) and meshfree methods of special properties including the upper bound properties. A G space is first defined to include discontinuous functions allowing the use of much more types of methods/techniques to create shape functions for numerical models; Properties and a set of important inequalities for G spaces are then proven in theory and analyzed in detail. We prove that the numerical methods developed based on the W2 formulation will be spatially stable, and convergent to exact solutions. We then present examples of some of the possible W2 models, and show the major properties of these models: 1) it is variationally consistent in a conventional sense, if the solution is sought in a H space (compatible cases); 2) it passes the standard patch test when the solution is sought in a G space with discontinuous functions (incompatible cases); 3) the stiffness of the discretized model is reduced compared to the FEM model and even the exact model, allowing us to obtain upper bound solutions with respect to both the FEM and the exact solutions; 4) the W2 models are less sensitive to the quality of the mesh, and triangular meshes can be used without any accuracy problems. These properties and theories have been confirmed numerically via examples solved using a number of W2 models including compatible and incompatible cases. An NS-PIM model is then used to establish a real-time computation procedure based on the reduced basis approximation. The real-time computation model is then used to inversely identify the interface property of a dental implant system.