Optimized incompressible smoothed particle hydrodynamics methods and validations

Ortega, Melissa Ramos; Beaudoin, Anthony; Huberson, S.

doi:10.1002/fld.4838

Cited by 3 publications

(3 citation statements)

References 87 publications

(212 reference statements)

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“…Although it seems still not as widely applicable as many other methods of the Eulerian approach, 3 SPH has become also a useful tool to explore fundamental mechanisms or simulate the industrial process in many applications. Various works have been reported contributing to the development of SPH, including various aspects such as the von Neumann stability analysis for one‐dimensional Eulerian equation, 4 incompressible methods, 5 approximation operators, 6 and multiphase flow modeling methods 7,8 . Additionally, a hybrid method combining the adaptive mesh refinement technique and the mesh‐free feature of the SPH has also been presented which uses a kernel discretization of volumes with a high‐order matrix gradient estimator and a Riemann solver acting over the overlapped region of the volumes 9 …”

Section: Introductionmentioning

confidence: 99%

A diffusion‐equation based kernel function for smoothed particle hydrodynamics: Methods and validations

Cao

Gui

Zhang

et al. 2023

Numerical Methods in Fluids

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A diffusion‐equation‐based kernel function (called the diffusive kernel) is proposed for flow and heat transfer simulation by the smoothed‐particle‐hydrodynamics (SPH) method. This new diffusive function has basic features of physics‐based, intrinsically conservative, and mathematically smoothing, because of a general solution of the diffusion equation. Three cases have been employed for method validation. One is the SOD's problem (a one‐dimensional case of the Riemann problem). The SPH simulation with the new kernel is compared to both analytical solutions and the SPH simulation by the third‐order B‐spline kernel. The second one is the dam‐break case to compare the performance of the cubic‐spline kernel, the quintic‐spline kernel, and the Wendland C2 kernel with the current diffusive kernel. The present kernel seems to perform as well as the well‐known Wendland C2 and the quintic kernels. The last case is natural convection in a concentric circular domain with temperature differences between the inner and outer concentric walls. Both the Gaussian kernel and the diffusive kernel were used for comparison and validation. Good consistency between numerical and analytical results, as well as experimental results, validates the good performance of the current diffusive kernel. After validation, it is clear that the diffusive kernel can simulate both the shock wave and natural convective heat transfer very well, and is much better than the conventional Gaussian kernel except for computational efficiency. The kernel profiles, together with their derivatives and integrals, are explored to explain why the diffusive kernel's performance is much better. Finally, to increase numerical efficiency, a fitted expression of the diffusive kernel is also given. The fitted diffusive kernel can reach the same level of computational efficiency as the Gaussian kernel while maintaining the basic advantages of the current diffusive kernel, which gives a choice for practical application.

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Section: Introductionmentioning

confidence: 99%

A diffusion‐equation based kernel function for smoothed particle hydrodynamics: Methods and validations

Cao

Gui

Zhang

et al. 2023

Numerical Methods in Fluids

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“…The computational cost then becomes been much higher than that of the WCSPH method 55‐57 . An optimization of ISPH methods has been proposed by Ramos Ortega et al 58 in 2020. A gain of CPU time is possible by solving the Poisson's equation on a Cartesian grid.…”

Section: Introductionmentioning

confidence: 99%

“…Thus it is not necessary to add a particle scale turbulence model in the ISPHP method 34,40 . And the optimization of the solving of Poisson's equation, proposed by Ramos Ortega et al 58 in 2020, is used in the ISPHP method to have a gain of CPU.…”

Section: Introductionmentioning

confidence: 99%

Modified incompressible smooth particle hydrodynamics in porous media method for modeling the damping of a waves train on an inclined porous structure

Ortega

Beaudoin

2021

Numerical Methods in Fluids

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In this work, the ISPHP method proposed by Akbari and Namin in 2013 has been modified by implementing the Taylor expansion of a classical smoothing function. The modified ISPHP method with the Taylor expansion of the smoothing function, the optimization of the solving of Poisson's equation and the wave maker, has been used to simulate the damping of a waves train on an inclined porous structure. The comparison between the numerical results obtained with the modified ISPHP method and the experimental data obtained by Carrasco et al. in 2020 has shown on the one hand that the modified ISPHP method could be used to study the damping of a waves train on an inclined porous structure and on the other hand that the dimensionless number χ could be used to characterize the energy transformations of the interaction of a waves train and an inclined porous structure.

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Analysis of high Reynolds free surface flows

Young

Lin

Tsai

2022

Journal of Mechanics

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In this paper, we will combine an upwind radial basis function-finite element with direct velocity–pressure formulation to study the two-dimensional Navier-Stokes equations with free surface flows. We will examine this formulation in an improved mixed-order finite element and localized radial basis function method. A particle tracking method and the arbitrary Lagrangian-Eulerian scheme will then be applied to simulate the two-dimensional high Reynolds free surface flows. An upwind improved finite element formulation based on a localized radial basis function differential quadrature (LRBFDQ) method is used to deal with high Reynolds number convection dominated flows. This study successfully obtained very high Reynolds number free surface flows, up to Re = 500 000. Finally, we will demonstrate and discuss the capability and feasibility of the proposed model by simulating two complex free surface flow problems: (1) a highly nonlinear free oscillation flow and (2) a large amplitude sloshing problem. Using even very coarse grids in all computing scenarios, we have achieved good results in accuracy and efficiency.

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Optimized incompressible smoothed particle hydrodynamics methods and validations

Cited by 3 publications

References 87 publications

A diffusion‐equation based kernel function for smoothed particle hydrodynamics: Methods and validations

A diffusion‐equation based kernel function for smoothed particle hydrodynamics: Methods and validations

Modified incompressible smooth particle hydrodynamics in porous media method for modeling the damping of a waves train on an inclined porous structure

Analysis of high Reynolds free surface flows

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