Topic
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 spectral element method based on Chebyshev polynomials is developed to predict the electromechanical dynamics of panels having arbitrary geometries and multiple surface-bonded piezo-patches.
7 citations
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01 Apr 2018
TL;DR: The MFPM is used to approximate the Stokes problem and numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.
Abstract: The Modified Finite Particle Method (MFPM) is a numerical method belonging to the class of meshless methods, nowadays widely investigated due to their characteristic of being capable to easily model large deformation and fluid-dynamic problems. Here we use the MFPM to approximate the Stokes problem. Since the classical formulation of the Stokes problem may lead to pressure spurious oscillations, we investigate alternative formulations and focus on how MFPM discretization behaves in those situations. Some of the investigated formulations, in fact, do not enforce strongly the incompressibility constraint, and therefore an important issue of the present work is to verify if the MFPM is able to correctly reproduce the incompressibility in those cases. The numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.
7 citations
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TL;DR: A meshfree Lagrangian particle method for the Landau-Lifshitz Navier-Stokes (LLNS) equations is developed and a numerical test for the random walk of standing shock wave has been considered for capturing the shock location.
7 citations
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TL;DR: An extension of the second GFDM method is presented, which allows for accounting for internal interfaces, associated with discontinuous coefficients, and results from numerical experiments illustrate the second order convergence of the proposed GFDM for interface problems.
Abstract: The aim of this paper is twofold. First, two generalized (meshfree) finite difference methods (GFDM) for the Poisson equation are discussed. These are methods due to Liszka and Orkisz (1980) [10] and to Tiwari (2001) [7]. Both methods are based on using moving least squares (MLS) approach for deriving the discretization. The relative comparison shows, that the second method is preferable because it is less sensitive to the topological restrictions on the nodes distribution. Next, an extension of the second method is presented, which allows for accounting for internal interfaces, associated with discontinuous coefficients. Results from numerical experiments illustrate the second order convergence of the proposed GFDM for interface problems.
7 citations
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TL;DR: The method of approximate particular solutions (MAPS) is used to solve the two‐dimensional Navier–Stokes equations and despite the use of relative coarse nodal distributions, numerical results show excellent agreement with respect to results reported in literature.
Abstract: The method of approximate particular solutions (MAPS) is used to solve the two-dimensional Navier–Stokes equations. This method uses particular solutions of a nonhomogeneous Stokes problem, with the multiquadric radial basis function as a nonhomogeneous term, to approximate the velocity and pressure fields. The continuity equation is not explicitly imposed since the used particular solutions are mass conservative. To improve the computational efficiency of the global MAPS, the domain is split into overlapped subdomains where the Schwarz Alternating Algorithm is employed using velocity or traction values from neighboring subdomains as boundary conditions. When imposing only velocity boundary conditions, an extra step is required to find a reference value for the pressure at each subdomain to guarantee continuity of pressure across subdomains. The Stokes lid-driven cavity flow problem is solved to assess the performance of the Schwarz algorithm in comparison to a finite-difference-type localized MAPS. The Kovasznay flow problem is used to validate the proposed numerical scheme. Despite the use of relative coarse nodal distributions, numerical results show excellent agreement with respect to results reported in literature when solving the lid-driven cavity (up to Re = 10,000) and the backward facing step (at Re = 800) problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 777–797, 2015
7 citations