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Three-Dimensional (3D) Numerical Modeling of Morphogenesis in Dehydrated Fruits and Vegetables
Published in Guangnan Chen, Advances in Agricultural Machinery and Technologies, 2018
C. M. Rathnayaka, H. C. P. Karunasena, Wiji Senadeera, Lisa Guan, Y. T. Gu
Meshfree approaches have proven to be stable as well as versatile with high accuracy and efficiency applicable to a wider range of problems (Belytschko et al., 1996). At present, there is a wide range of meshfree methods developed to suit different applications (Liu, 2010; Liu and Liu, 2003b; Liu and Gu, 2005; Li and Liu, 2002; Belytschko et al., 1996; Idelsohn and Onate, 2006; Nguyen et al., 2008; Frank and Perré, 2010). Among them, the most popular techniques are: Smoothed-Particle Hydrodynamics (SPH) (Liu and Liu, 2010), Element-Free Galerkin (EFG) method (Belytschko, Lu, and Gu, 1994), Point Interpolation Method (PIM) (Liu and Gu, 2002), Meshless Local Petrov-Galerkin (MPLG) method (Atluri and Zhu, 1998), Local Radial Point Interpolation Method (LRPIM) (Liu and Gu, 2001), and the boundary point interpolation method (BPIM) (Liu and Gu, 2004).
Computational Models for Water Resource Management
Published in Satya Prakash Maurya, Akhilesh Kumar Yadav, Ramesh Singh, Modeling and Simulation of Environmental Systems, 2023
Meshfree models and are recently being applied to many groundwater-related problems (Mategaonkar and Eldho, 2011; Singh et al., 2016; Anshuman and Eldho 2020). Due to the presence of mesh/grid, the mesh-based methods have disadvantages such as difficulty in representing irregular domain, instabilities in advection and reaction dominant problems such as oscillation and numerical dispersion etc. (Liu and Gu, 2005). In contrast to mesh/grid-based methods, meshfree methods use a set of scattered nodes within the domain without any connectivity to adjacent nodes. Instead, these methods use a local support domain around each node (see Figure 1.1c).
Meshfree dynamic analysis of functionally graded carbon nanotube reinforced polymer sandwich beams under harmonic moving loads
Published in Australian Journal of Mechanical Engineering, 2022
Alireza Sayyidmousavi, Mehrdad Foroutan, Zouheir Fawaz
The main idea of the Finite Element Method (FEM) is to discretise the problem domain into small segments, called elements. This discretizing process, known as mesh generation, being computationally costly and time-consuming, is one of the main drawbacks of this method. Moreover, problems involving large deformation or material breakage, in which the elements get distorted, require adaptive meshing. Recently, mesh free methods have been used as an efficient alternative numerical tool to solve different initial and boundary-value problems. The main advantage of meshfree methods compared to the FEM is that the computational domain is modelled by only a set of scattered nodes that are not connected to form a closed polygon, thereby eliminating the mesh generation phase. This results in considerable saving in both time and computation. In meshfree methods, the field variable is calculated at the gauss point rather than at a certain node. The Gauss point is, in fact, any point of interest in the problem domain. The field variable at any point of interest is approximated using a group of field nodes in the so-called support domain of that very point. Also, the fact that in meshfree methods, the material variation is captured at the integration or gauss points makes them a suitable tool particularly for modelling smooth material property change in FG materials without the need for post-processing the results (Qian and Ching 2011).
Numerical simulation of free convection of MHD non-Newtonian nanofluid within a square wavy enclosure using Meshfree method
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2020
Most of the mathematical models are transformed in nonlinear partial differential equations which can be managed more efficiently by numerical schemes. These numerical schemes are divided into two categories: Grid dependent and Grid independent. Grid-dependent methods are namely finite difference method, finite volume method, finite element method whereas Grid independent method contains various Meshfree methods. Meshfree methods play an important role where the domain is irregular e.g. bursting of stars, propagation of fire, change in nature of flow and phase change problems. Details of the method are given in Liu [20]. Singh and Bhargava [21], Prasad et al. [22], Goyal and Bhargava [23] and Alvarez-Hostos et al. [24] considered the irregular problem domain and they solved the problem by mesh free method. The main objective of this article is to simulate the flow and heat transfer in an irregular domain: wavy square enclosure filled with power-law nanofluid with an efficient numerical Meshfree approach, as a novel contribution.
Meshfree Galerkin method for a rotating Euler-Bernoulli beam
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2018
Vijay Panchore, Ranjan Ganguli, S N Omkar
Meshfree methods are based on the distribution of nodal points in the domain. Figure 4 illustrates the nodal distribution along the length of the beam in a single local support domain Ω(1)s.