A Study on Stable Regularized Moving Least-Squares Interpolation and Coupled with SPH Method

The smoothed particle hydrodynamics (SPH) method has been popularly applied in various fields, including astrodynamics, thermodynamics, aerodynamics, and hydrodynamics. Generally, a high-precision interpolation is required to calculate the particle physical attributes and their derivatives for the boundary treatment and postproceeding in the SPH simulation. However, as a result of the truncation of kernel function support domain and irregular particle distribution, the interpolation using conventional SPH interpolation experiences low accuracy for the particles near the boundary and free surface. To overcome this drawback, stable regularized moving least-squares (SRMLS) method was introduced for interpolation in SPH. The surface fitting studies were performed with a variety of polyline bases, spatial resolutions, particle distributions, kernel functions, and support domain sizes. Numerical solutions were compared with the results using moving least-squares (MLS) and three SPH methods, including CSPH, K2SPH, and KGFSPH, and it was found that SRMLS not only has nonsingular moment matrix, but also obtains high-accuracy result. Finally, the capability of the algorithm coupled with SRMLS and SPH was illustrated and assessed through several numerical tests.

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Moving least squares particle hydrodynamics method for Burgers’ equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.03.040 ◽

2019 ◽

Vol 356 ◽

pp. 362-378 ◽

Cited By ~ 1

Author(s):

Fangyan Fu ◽

Jiao Li ◽

Jun Lin ◽

Yanjin Guan ◽

Fuzheng Gao ◽

...

Keyword(s):

Least Squares ◽

Burgers Equation ◽

Moving Least Squares ◽

Particle Hydrodynamics

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Numerical solutions of the GEW equation using MLS collocation method

International Journal of Modern Physics C ◽

10.1142/s0129183117500115 ◽

2017 ◽

Vol 28 (01) ◽

pp. 1750011

Author(s):

Ayşe Gül Kaplan ◽

Yılmaz Dereli

Keyword(s):

Least Squares ◽

Collocation Method ◽

Solitary Waves ◽

Numerical Solutions ◽

Rates Of Convergence ◽

Numerical Results ◽

Moving Least Squares ◽

Test Problems ◽

Least Squares Collocation ◽

Energy And Momentum

In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known [Formula: see text], [Formula: see text] error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.

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Welding Window: Comparison of Deribas’ and Wittman’s Approaches and SPH Simulation Results

Metals ◽

10.3390/met9121323 ◽

2019 ◽

Vol 9 (12) ◽

pp. 1323 ◽

Cited By ~ 2

Author(s):

Yulia Yu. Émurlaeva ◽

Ivan A. Bataev ◽

Qiang Zhou ◽

Daria V. Lazurenko ◽

Ivan V. Ivanov ◽

...

Keyword(s):

Numerical Simulation ◽

High Velocity ◽

High Velocity Impact ◽

Sph Method ◽

Velocity Impact ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Impact Welding ◽

Simulation Results ◽

Sph Simulation

A welding window is one of the key concepts used to select optimal regimes for high-velocity impact welding. In a number of recent studies, the method of smoothed particle hydrodynamics (SPH) was used to find the welding window. In this paper, an attempt is made to compare the results of SPH simulation and classical approaches to find the boundaries of a welding window. The experimental data on the welding of 6061-T6 alloy obtained by Wittman were used to verify the simulation results. Numerical simulation of high-velocity impact accompanied by deformation and heating was carried out by the SPH method in Ansys Autodyn software. To analyze the cooling process, the heat equation was solved using the finite difference method. Numerical simulation reproduced most of the explosion welding phenomena, in particular, the formation of waves, vortices, and jets. The left, right, and lower boundaries found using numerical simulations were in good agreement with those found using Wittman’s and Deribas’s approaches. At the same time, significant differences were found in the position of the upper limit. The results of this study improve understanding of the mechanism of joint formation during high-velocity impact welding.

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Dual-Support Smoothed Particle Hydrodynamics for Elastic Mechanics

International Journal of Computational Methods ◽

10.1142/s0219876217500396 ◽

2017 ◽

Vol 14 (04) ◽

pp. 1750039 ◽

Cited By ~ 4

Author(s):

Zili Dai ◽

Huilong Ren ◽

Xiaoying Zhuang ◽

Timon Rabczuk

Keyword(s):

Linear Transformation ◽

Smoothed Particle Hydrodynamics ◽

Three Dimensions ◽

Benchmark Problems ◽

Sph Method ◽

Particle Hydrodynamics ◽

Sph Model ◽

Smoothed Particle ◽

Support Domain ◽

Elastic Mechanics

In the standard smoothed particle hydrodynamics (SPH) method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this paper. First of all, a Lagrangian kernel is introduced to eliminate spurious distortions of the domain of material stability, and the gradient is corrected by a linear transformation so that linear completeness is satisfied. Then, concepts of support and dual-support are defined to deal with the unbalanced interactions between the particles with different support domains. Several benchmark problems in one, two and three dimensions are tested to verify the accuracy of the modified SPH model and highlight its advantages over the standard SPH method through comparisons.

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SPH Simulation of Hydrodynamic Forces on Subsea Pipelines

Volume 7: CFD and VIV; Offshore Geotechnics ◽

10.1115/omae2011-50029 ◽

2011 ◽

Author(s):

Kourosh Abdolmaleki

Keyword(s):

Hydrodynamic Forces ◽

Forced Oscillations ◽

Sph Method ◽

Flat Bottom ◽

Extreme Load ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Sph Simulation ◽

Subsea Pipelines ◽

Supercritical Flows

Hydrodynamic forces on subsea pipelines are simulated using Smoothed Particle Hydrodynamics (SPH) method. The objective is to assess the suitability of this method for common sub-sea engineering problems. The standard SPH formulation is used for simulation of cases with high KC and Re numbers, where the flow becomes turbulent with laminar or partially turbulent boundary layer. The numerical model includes a pipe section with smooth surface resting on a flat bottom. The pipe is exposed to various combinations of regular waves and current. The current is modelled as a steady flow of fluid particles and the waves are represented by forced oscillations of the pipe at defined frequencies and amplitudes. The selected KC and Re numbers produces subcritical and supercritical flows, which simulate extreme load cases on pipelines. In subcritical flows, the estimated forces on the pipeline agree well with experimental data. In supercritical flows with high KC and Re values, a relatively finer particle resolution is required in order to capture multiple harmonics of oscillating lift force. In conclusion, the SPH method could satisfactorily predict hydrodynamic forces on pipelines for the cases investigated.

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A New Revised Scheme for SPH

International Journal of Computational Methods ◽

10.1142/s0219876218500354 ◽

2018 ◽

Vol 15 (05) ◽

pp. 1850035

Author(s):

Rahmatjan Imin ◽

Ahmatjan Iminjan ◽

Azhar Halik

Keyword(s):

Taylor Series Expansion ◽

Sph Method ◽

One Dimensional ◽

Convection Diffusion ◽

Kernel Approximation ◽

Interpolation Of Functions ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Support Domain ◽

Smoothed Kernel

Based on the smoothed kernel approximation of the Smoothed Particle Hydrodynamics (SPH) method and Taylor series expansion, a new revised scheme for SPH method is proposed which significantly improves its accuracy, especially near the boundaries where the particle points do not entirely cover the compact support domain of kernel function and particles are irregularly distributed. The revised scheme is derived up to the first-and second-order derivatives both in one-dimensional and multi-dimensional cases. In order to demonstrate the ability of the proposed revised scheme, the scheme is applied to the interpolation of functions and the numerical solution of the convection–diffusion equations both in one- and two-dimensional cases.

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NUMERICAL SOLUTIONS OF THE NONLINEAR POROUS MEDIA EQUATION BASED ON HIGH EXPLORATION PARTICLE SWARM OPTIMIZATION AND MOVING LEAST SQUARES

Journal of the Serbian Society for Computational Mechanics ◽

10.24874/jsscm.2020.14.02.03 ◽

2020 ◽

Vol 14 (2) ◽

pp. 31-50

Author(s):

Mohammad Javad Mahmoodabadi ◽

Ali Reza Ghanizadeh

Keyword(s):

Porous Media ◽

Particle Swarm Optimization ◽

Least Squares ◽

Numerical Solutions ◽

Initial Conditions ◽

Particle Swarm ◽

Moving Least Squares ◽

Porous Media Equation ◽

Swarm Optimization ◽

Media Equation

In this study, a new numerical method based on the combination of High Exploration Particle Swarm Optimization (HEPSO) and Moving Least Squares (MLS) is introduced to solve nonlinear porous media equations. The MLS scheme is employed to describe an appropriate discretized function, and the penalty method is implemented to convert the constrained problem into an unconstrained one via satisfying the initial conditions. The identified objective function is minimized by the HEPSO to find the approximated nodal values for the nonlinear porous media equation. In order to illustrate the effectiveness of the HEPSO, the optimization trajectories are compared with those of a Standard Particle Swarm Optimization (SPSO) algorithm. Moreover, comparisons are made between the exact solution and the introduced strategy to expose the accuracy, effectiveness and simplicity of the proposed method.

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