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Meshfree methods

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


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Journal ArticleDOI
TL;DR: In this paper, a new approach to the solution of boundary value problems within the so-called fictitious domain method philosophy is proposed, which avoids well-known shortcomings of other methods of this type.
Abstract: A new approach to the solution of boundary value problems within the so-called fictitious domain method philosophy is proposed, which avoids well-known shortcomings of other methods of this type, i...

5 citations

DOI
01 Jun 2018
TL;DR: In this paper, a novel coupling of three state-of-the-art particle methods, capable of simulating heat transfer in multiphase flows with minimum error, is presented.
Abstract: This article presents a novel coupling of three state-of-the-art particle methods, capable of simulating heat transfer in multiphase flows with minimum error. The idea originates from increasing the robustness of the geometric features required to calculate physical quantities, such as the boundary conditions in the heat equation and the surface tension force in Navier-Stokes equations. The workability of this new approach for handling thermal effects in complex moving interfaces is examined with a numerical test case wherein multiple scenarios such as internal flow, bursting at free surface as well as bubble evolutionary motions occur. Performing a benchmark comparison with the reference model implemented in COMSOL Multiphysics®, a markedly improved mass conservation using the proposed particle-based solver is observed. This, in turn, results in a more realistic and accurate approximation of the temperature.

5 citations

Dissertation
12 May 2014
TL;DR: This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems, and indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.
Abstract: This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods. The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique. The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique. Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored. All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the Fraeijs de Veubeke variational principle is used to approximate the displacement field, the stress field and the strain field in the natural neighbor method.
Abstract: The natural neighbour method can be considered as belonging to the meshless methods. Classically, the development of this method is based on the virtual work principle. In the present paper, we use the natural neighbour method for 2D domains starting from the Fraeijs de Veubeke variational principle and we approximate separately the displacement field, the stress field and the strain field: the assumed strains and the assumed stresses are constant over each Voronoi cell, the assumed surface reactions are constant along the edge where the displacements are imposed, while the assumed displacements are interpolated by Laplace interpolants. In the absence of body forces, it is shown that the calculation of integrals on the area of the solid domain can be avoided: only integrals on the edges of the Voronoi cells are necessary. On the other hand, displacements can be imposed in the average sense on some boundaries of the domain. Patch tests and some applications in the elastic domain are given in the paper and show the effectiveness of the method. Copyright © 2007 John Wiley & Sons, Ltd.

5 citations

Journal ArticleDOI
TL;DR: In this paper, a new approach for the numerical solution of linear and nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal boundary conditions is proposed.
Abstract: This paper is concerned with the development of a new approach for the numerical solution of linear and nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal boundary conditions. Proper finite-difference approximations are utilized to discretize the time variable. Then, the weak equations of resultant elliptic type PDEs are constructed on local subdomains. These local weak equations are discretized by using the multiquadric (MQ) radial basis function (RBF) approximation where an iterative procedure is proposed to treat the nonlinear terms in each time step. Numerical test problems are given to verify the accuracy of the obtained numerical approximations and stability of the proposed method versus the parameters of the nonlocal boundary conditions.

5 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897