Constructing smoothing functions in smoothed particle hydrodynamics with applications

Liu, M. B.; Liu, G. R.; Lam, K.Y.

doi:10.1016/s0377-0427(02)00869-5

Cited by 219 publications

(125 citation statements)

References 18 publications

Supporting

Mentioning

123

Contrasting

Unclassified

Order By: Relevance

“…The smoothing function is sometimes referred to as kernel or kernel function, and it should satisfy some basic requirements, such as normalization condition, compact supportness, and Delta function behavior. This conditions are needed to ensure convergence and reproducibility of function approximation A detailed discussion on the smoothing function, its basic requirements and constructing conditions can found in [20,21]. In this paper, the frequently used cubic spline is employed for general purposes.…”

Section: Sph Equations Of Motionmentioning

confidence: 99%

An improved SPH method for modeling liquid sloshing dynamics

Shao

Liu

et al. 2012

Computers & Structures

Self Cite

206

View full text Add to dashboard Cite

Section: Sph Equations Of Motionmentioning

confidence: 99%

An improved SPH method for modeling liquid sloshing dynamics

Shao

Liu

et al. 2012

Computers & Structures

Self Cite

206

View full text Add to dashboard Cite

“…Besides the above properties, other requirements may also required in different literatures such as monotonically decreasing condition, even function condition, smoothing condition, and non-negativity condition [21].…”

Section: Properties Of a Kernel Functionmentioning

confidence: 99%

“…According to their assessment, bell-shaped kernels perform better than kernels with other shapes and no kernel function is significantly better than the cubic spline. Liu et al [21] presented a general approach to construct analytical kernel functions. They also constructed a new quadric kernel function which was applied to the one dimensional shock problem and a one dimensional TNT detonation problem.…”

Section: Introductionmentioning

confidence: 99%

A new kernel function for SPH with applications to free surface flows

Yang

Peng

Liu

2014

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

a b s t r a c tSmoothed particle hydrodynamics (SPH) is a popular meshfree Lagrangian particle method, which uses a kernel function for numerical approximations. The kernel function is closely related to the computational accuracy and stability of the SPH method. In this paper, a new kernel function is proposed, which consists of two cosine functions and is referred to as double cosine kernel function. The newly proposed double cosine kernel function is sufficiently smooth, and is associated with an adjustable support domain. It also has smaller second order momentum, and therefore it can have better accuracy in terms of kernel approximation. SPH method with this double cosine kernel function is applied to simulate a dam-break flow and water entry of a horizontal circular cylinder. The obtained SPH results agree very well with the experimental results. The double cosine kernel function is also comparatively studied with two frequently used SPH kernel functions, Gaussian and cubic spline kernel functions.

show abstract

“…al., 1994;Krongauz & Belytschko 1997), Moving Least Square Particle Hydrodynamics (Dilts, 1999). An interesting method to ensure j-th order consistency has been proposed by (Liu et al, 2003b). Using the Taylor series expansion for the kernel…”

Section: J-th Order Consistencymentioning

confidence: 99%