A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems

Jiang, Tao; Ouyang, Jie; Ren, Jiaojiao; Yang, Binxin; Xu, Xiaozhong

doi:10.1016/j.cpc.2011.08.016

Cited by 29 publications

(17 citation statements)

References 38 publications

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“…However, as particles move and change their spatial position, additional numerical errors are introduced. Aiming to improve this problem, a number of remedies have been proposed and analyzed . Among these methods, and also following , the procedure proposed by Oger et al is implemented here:

bold-italicL {(bold-italicr)}_{i} = {(\begin{matrix} center \\ center \sum_{j} V_{j} (x_{j} - x_{i}) \frac{\partial w_{i j}}{\partial x} & center \sum_{j} V_{j} (x_{j} - x_{i}) \frac{\partial w_{i j}}{\partial y} \\ center \sum_{j} V_{j} (y_{j} - y_{i}) \frac{\partial w_{i j}}{\partial x} & center \sum_{j} V_{j} (y_{j} - y_{i}) \frac{\partial w_{i j}}{\partial y} \end{matrix})}^{- 1},

\nabla {\overset{true˜}{w}}_{i j} = bold-italicL {(bold-italicr)}_{i} \nabla w_{i j},

where L is the kernel gradient correction operator, x and y denote the horizontal and vertical coordinates of a particle, and V represents the volume of the particle, which is directly calculated here from m/ρ .…”

Section: Sph Methodologymentioning

confidence: 99%

See 1 more Smart Citation

A detailed study of lid‐driven cavity flow at moderate Reynolds numbers using Incompressible SPH

Khorasanizade¹,

Sousa²

2014

Numerical Methods in Fluids

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SUMMARY Lid‐driven cavity flow at moderate Reynolds numbers is studied here, employing a mesh‐free method known as Smoothed Particle Hydrodynamics (SPH). In a detailed study of this benchmark, the incompressible SPH approach is applied together with a particle shifting algorithm. Additionally, a new treatment for no‐slip boundary conditions is developed and tested. The use of the aforementioned numerical treatment for solid walls leads to significant improvements in the results with respect to other SPH simulations carried out with similar spatial resolution. However, the effect of spatial resolution is not considered in the present study as the number of particles used in each case was kept constant, approximately reproducing the same resolutions employed in reference studies available in the literature as well. Altogether, the detailed comparisons of field variables at discreet points demonstrate the accuracy and robustness of the new SPH method. Copyright © 2014 John Wiley & Sons, Ltd.

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bold-italicL {(bold-italicr)}_{i} = {(\begin{matrix} center \\ center \sum_{j} V_{j} (x_{j} - x_{i}) \frac{\partial w_{i j}}{\partial x} & center \sum_{j} V_{j} (x_{j} - x_{i}) \frac{\partial w_{i j}}{\partial y} \\ center \sum_{j} V_{j} (y_{j} - y_{i}) \frac{\partial w_{i j}}{\partial x} & center \sum_{j} V_{j} (y_{j} - y_{i}) \frac{\partial w_{i j}}{\partial y} \end{matrix})}^{- 1},

\nabla {\overset{true˜}{w}}_{i j} = bold-italicL {(bold-italicr)}_{i} \nabla w_{i j},

Section: Sph Methodologymentioning

confidence: 99%

“…However, as particles move and change their spatial position, additional numerical errors are introduced. Aiming to improve this problem, a number of remedies have been proposed and analyzed [28][29][30][31]. Among these methods, and also following [5,7], the procedure proposed by Oger et al [28] is implemented here:…”

Section: Kernel Correctionsmentioning

confidence: 99%

A detailed study of lid‐driven cavity flow at moderate Reynolds numbers using Incompressible SPH

Khorasanizade¹,

Sousa²

2014

Numerical Methods in Fluids

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“…Although most SPH simulations are quite robust and can deal with discontinuities in a natural way, there are some notable downsides, too: SPH methods can suffer from instabilities (mostly due to particle clustering), while their accuracy can be inferior to mesh-based methods. There are several correction mechanisms available and still being developed to cope with these problems [13,14], yet usually at the expense of a substantially higher computational cost. Nevertheless, the big advantage of SPH is that a wide range of physical aspects are relatively easy implemented in a particle simulator.…”

Section: Introductionmentioning

confidence: 99%

Solving microscopic flow problems using Stokes equations in SPH

Liedekerke

Smeets

Odenthal

et al. 2013

Computer Physics Communications

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Starting from the Smoothed Particle Hydrodynamics method (SPH), we propose an alternative way to solve flow problems at a very low Reynolds number. The method is based on an explicit drop out of the inertial terms in the normal SPH equations, and solves the coupled system to find the velocities of the particles using the conjugate gradient method. The method will be called NSPH which refers to the non-inertial character of the equations. Whereas the time-step in standard SPH formulations for low Reynolds numbers is linearly restricted by the inverse of the viscosity and quadratically by the particle resolution, the stability of the NSPH solution benefits from a higher viscosity and is independent of the particle resolution. Since this method allows for a much higher time-step, it solves creeping flow problems with a high resolution and a long timescale up to three orders of magnitude faster than SPH. In this paper, we compare the accuracy and capabilities of the new NSPH method to canonical SPH solutions considering a number of standard problems in fluid dynamics. In addition, we show that NSPH is capable of modeling more complex physical phenomena such as the motion of a red blood cell in plasma.

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“…However, SSPH retains terms up to second‐order derivatives in the Taylor series expansion of a function. As, for SSPH method it requires inverting a 6 × 6 matrix in 2D spaces and is complicated for them be extended to complex free surface flows problems . Huang et al proposed a kernel gradient free (KGF) SPH method in which the kernel gradient is not necessary in the whole computation process.…”

Section: Introductionmentioning

confidence: 99%

An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

Huang

Lei

Liu

et al. 2015

Numerical Methods in Fluids

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Summary The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF‐SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF‐SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF‐SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF‐SPH method avoids nested approximation of first order derivatives, and keeps the good feature of ‘kernel gradient free’. The two‐dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF‐SPH and improved KGF‐SPH. The numerical results show that the improved KGF‐SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF‐SPH. Copyright © 2015 John Wiley & Sons, Ltd.

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A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems

Cited by 29 publications

References 38 publications

A detailed study of lid‐driven cavity flow at moderate Reynolds numbers using Incompressible SPH

A detailed study of lid‐driven cavity flow at moderate Reynolds numbers using Incompressible SPH

Solving microscopic flow problems using Stokes equations in SPH

An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

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