Papers by Keyword: Meshless Method

Abstract: This work presents a hybrid formulation combining the Method of Fundamental Solutions (MFS) and the Method of Particular Solutions (MPS) coupled with an implicit Finite Difference Method (FDM) to simulate the transient heat conduction in a two-layer domain composed of a steel tool and an epoxy resin. The proposed approach incorporates a non-homogeneous source term in the governing equation, allowing the analysis of the curing heat release within the resin layer while maintaining a meshless boundary-based structure. Sequential numerical tests were performed to empirically assess the influence of key hyper-parameters number and position of source points, distance parameters, and the Tikhonov regularization factor on the stability and accuracy of the method. The MFS-MPS/FDM model showed excellent agreement with the finite element results reported by Dei Sommi et al., achieving low RMSE and MAE values relative to the thermal scale of the process. These results confirm the robustness and predictive capability of the MFS in capturing transient thermal evolution even in the presence of a source term, although its performance remains sensitive to the proper calibration of numerical hyper-parameters.

Abstract: The numerical simulation of the bending analysis of Functionally Graded Beam (FGB) is based on a truly meshless Smoothed Hydrodynamic Particle (SPH) method, where the inherent deficiencies were reduced by introducing Corrective Smoothed Particle Method (CSPM) and Total Lagrangian (TL) formulation. The mechanical and physical properties through the thickness of FGB were explained using a power law. The performance of the present SPH method was validated by comparison of solutions of numerical application with the analytical solutions.

Abstract: Fiber orientation angles optimization is carried out for maximum fundamental frequency of clamped laminated composite plates using the genetic algorithm. The meshless method is utilized to calculate the fundamental frequency of clamped laminated composite plates. In the present paper, the maximum fundamental frequency is an objective function; design variables are a set of fiber orientation angles in the layers. The examples of square laminated plates are considered. The results for the optimal fiber orientation angles and the maximum fundamental frequencies of the 2-layer plates are presented.

Abstract: This paper presents an application of the Finite Volume Particle Method to incompressible flows. The two-dimensional incompressible Navier-Stokes solver is based on Chorin’s projection method with finite volume particle discretization. The Finite Volume Particle Method is a meshless method for fluid dynamics which unifies advantages of particle methods and finite volume methods in one scheme. The method of manufactured solutions is used to examine the global discretization error and finally a comparison between finite volume particle method simulations of an incompressible flow around a fixed circular cylinder and the numerical simulations with the CFD code ANSYS FLUENT 14.0 is presented.

Abstract: The ballistic simulation attempted in this work is among the most difficult as both the projectile and the target experience significant deformations. Traditionally these simulations have been performed using a Lagrangian approach, i.e. a deformable mesh with large mesh deformations. There are three often used techniques when studying ballistic problems with the Lagrangian method: remeshing (generally not available for 3D hexahedra meshes), the 'pilot hole' technique and material erosion. Because these techniques imply element removal, in order to allow the calculation to continue, the Lagrangian method lacks a physical basis. Moreover, no general guidance exists for selecting one of the three techniques mentioned before. The Smoothed Particle Hydrodynamic method as implemented in the commercial code LS-DYNA has been used in this paper to solve the problem of the impact between different caliber projectiles and various types of metal targets. The results are compared to those produced by dynamic analysis using conventional finite element methods with material erosion as implemented in LS-DYNA.

Abstract: In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Abstract: A comprehensive multiphysics model has been developed to describe the effect of the low frequency electromagnetic field (LFEM) [1, on solidification in the hot-top Direct-Chill (DC) casting [ of round aluminium alloy billets. The volume averaged equations and the rigid solid phase assumption are assumed for fluid flow and heat transfer [. The electromagnetic induction equation for the field imposed by the coil is solved using the diffuse approximate method (DAM), structured in axial symmetry with Gaussian weight function, 6 polynomial basis and 9 nodded domains. The heat, mass, and momentum transfer equations are solved in primitive variables by meshless [ method using 5 nodded domains of influence and 5 scaled multiquadrics radial basis functions, using collocation. Explicit time stepping is used. Pressure-velocity coupling is performed by the fractional step method. The effects of intensity and frequency of the LFEM [ on the velocity and temperature fields is investigated. A comparison of the calculated results with different LFEM field process variables with that of the conventional hot-top DC casting process indicates that the velocity patterns, the temperature profiles, and the shape of the sump could be modified remarkably.

Abstract: There is a continuously developing need for benchmarking of solidification simulations - from the theoretical [1] as well as from the applied [2] points of view. The history of related benchmarking shows differences of the results between different numerical methods, and differences in comparison with the experiments when solving even quite simple solidification situations. The present benchmark test proposes macrosegregation [3] upgrades to the verification benchmark for continuous casting of steel, first presented in [2]. The paper represents guidelines for the presentation of the numerical method, discretisation and results and shows a reasonable comparison between a commercial finite volume based code and our in-house developed meshless method based code.

Abstract: A meshless local Petrov-Galerkin method (MLPG) using Heaviside step function as a test function for solving the biharmonic equation with subjected to boundary of the second kind is presented in this paper. Nodal shape function is constructed by the radial point interpolation method (RPIM) which holds the Kroneckers delta property. Two-field variables local weak forms are used in order to decompose the biharmonic equation into a couple of Poisson equations as well as impose straightforward boundary of the second kind, and no special treatment techniques are required. Selected engineering numerical examples using conventional nodal arrangement as well as polynomial basis choices are considered to demonstrate the applicability, the easiness, and the accuracy of the proposed method. This robust method gives quite accurate numerical results, implementing by maximum relative error and root mean square relative error.

Abstract: This paper formulates a radial basis function meshless method for the numerical simulation of the advection-diffusion problems. The spatial derivatives are approximated by RBF collocation technique whereas the temporal derivatives are discretized using the Crank-Nicholson method. Corresponding boundary conditions are enforced analytically at a discrete set of boundary nodes. The performances of the present method are demonstrated through their application to an advection-diffusion problem.