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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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TL;DR: In this paper, a meshless method based on the radial basis functions was proposed to solve one-dimensional stochastic heat and advection-diffusion equations, where the spatial derivatives were approximated by Kansa approach.
Abstract: With respect to wide range of applications of stochstic partial differential equation (SPDE) and high ability of meshless methods to solve complicated problems, in this paper, an efficient numerical method for the time fractional SPDE, formulated with Caputo’s fractional derivative, based on meshless methods is presented. This article presents a meshless method based on the radial basis functions to solve one-dimensional stochastic heat and advection–diffusion equations. In here, first, we approximate the time fractional derivative of the mentioned equations by a scheme of order $$ \mathsf {O}(\tau ^{2-\alpha }) $$ , $$ 0<\alpha <1 $$ then the spatial derivatives are approximated by Kansa approach. Numerical examples are presented to show the efficiency and effectiveness of the proposed method in solving fractional SPDEs.

6 citations

01 Jan 2002
TL;DR: In this paper, the Corrected Smooth Particle Hydrodynamics (CSPH) method is used to simulate fluid flow in the high pressure die casting cavity, where the quantities determining the flow are localized on set of particles, which move with the flow.
Abstract: Simulation of mould filling in high pressure die casting has been an attractive area of research for many years. Several numerical methodologies have been adopted in the past to study the flow behaviour of the molten metal inside the die cavities. However, many of these methods require stationary mesh or grid which limits their ability in simulating highly dynamic and transient flows encountered in high pressure die casting processes. In recent years, the advent of meshfree methods have led to the opening of new avenues in numerical computational field. Consequently, particle based methods have emerged as an attractive alternative for modeling mould filling simulation in pressure die casting processes. In this paper the Corrected Smooth Particle Hydrodynamics (CSPH) method is used to simulate fluid flow in the high pressure die casting cavity. CSPH is a Lagrangian method based on Smooth Particle Hydrodynamics (SPH) techniques. In CSPH method, the quantities determining the flow are localised on set of particles, which move with the flow. This enables the method to easily follow complex free surfaces, including fragmentation. This paper mainly deals with the formulation of governing equation required CSPH simulation of high pressure die casting process and presents a number of numerical results to demonstrate the capabilities of the numerical model.

6 citations

Journal ArticleDOI
TL;DR: The literature shows that meshless methods have the potential to be the future of biomechanical computational simulation and are capable of producing smoother and much more accurate stress and strain fields.
Abstract: Meshless methods are advanced discretization techniques, which permit to discretize the problem physical domain with an unstructured nodal cloud. This discretization flexibility allows obtaining the geometrical model directly from medical images, such as computerized axial tomography (CAT) scans or magnetic resonance imaging (MRI) techniques. Then, it is possible to analyse straightforwardly the biomechanical behaviour of biological structures. When compared with other mesh-dependent discretization techniques, meshless methods are capable of producing smoother and much more accurate stress and strain fields. The literature shows that meshless methods have the potential to be the future of biomechanical computational simulation.

6 citations

Journal ArticleDOI
TL;DR: A meshfree postprocessing for the computation of field lines suggests itself in the case of fast boundary element methods because field values are only calculated and stored in points, which are absolutely necessary for field line computations.
Abstract: A meshfree postprocessing for the computation of field lines suggests itself in the case of fast boundary element methods. Field values are only calculated and stored in points, which are absolutely necessary for field line computations. Hence, the total amount of processed data is dramatically reduced in comparison to a mesh-based approach along with precomputed field values in all mesh nodes. An automatic and robust domain detection method enables reliable identifications of intersections of field lines with domain boundaries even in the case of complex-shaped surfaces. A combination of automatic domain detection and adaptive step size control of the underlying Runge–Kutta–Fehlberg method results in correctly and efficiently computed field lines, including sharp bends at domain boundaries.

6 citations

Journal ArticleDOI
TL;DR: It is shown that FIM compares favorably with FEM and offers a number of advantages and the use of the optimum parameter provides better precision than the other two methods with similar computational cost.

6 citations


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