Non-smooth kernels for meshfree methods in fluid dynamics

Belley, Jean-Marc; Belley, P.; Colin, Fabrice; Egli, Richard

doi:10.1016/j.camwa.2009.06.002

Cited by 3 publications

(6 citation statements)

References 15 publications

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“…Similar reproducing conditions listed below are satisfied, by the first and second derivatives, respectively (for additional information, see for instance [11])…”

Section: One-dimensional Casementioning

confidence: 77%

“…As it will be demonstrated in this section, it is even possible to use piecewise constant kernels (see [11]). We briefly recall the main definitions and properties of one-dimensional kernels before turning our attention to the two-dimensional case.…”

Section: Piecewise Constant Kernelsmentioning

confidence: 97%

“…We recall the definition of one-dimensional kernels, used in [11], for the evaluation of a function, and its first and second derivatives. For an interval [x −h, x +h] ⊂ R, let h be the discontinuous function on R defined by…”

Section: One-dimensional Casementioning

confidence: 99%

“…Because of the simplicity of one-dimensional piecewise constant kernels, the two-dimensional kernels needed to approximate first-and second-order 873 partial derivatives, can be defined as the products of one-dimensional kernels (see [11,12]). The resulting kernels, denoted respectively by K h , K…”

Section: Two-dimensional Extensionmentioning

confidence: 99%

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A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

Colin

Egli

Mounim

2011

Numerical Meth Engineering

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SUMMARYIn this paper, we develop a meshfree particle-based method for convection-diffusion problems. Discretization is performed by using piecewise constant kernels. The stabilized scheme is based on a new upwind kernel. We show that accurate and stable scheme can be obtained by using purpose-built kernels. It also shown that under some conditions the classical optimal finite difference scheme can be derived by the new method. Several numerical tests validate the method.

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“…Similar reproducing conditions listed below are satisfied, by the first and second derivatives, respectively (for additional information, see for instance [11])…”

Section: One-dimensional Casementioning

confidence: 77%

Section: Piecewise Constant Kernelsmentioning

confidence: 97%

Section: One-dimensional Casementioning

confidence: 99%

Section: Two-dimensional Extensionmentioning

confidence: 99%

See 2 more Smart Citations

A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

Colin

Egli

Mounim

2011

Numerical Meth Engineering

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“…Authors of introduced piecewise constant kernels to approximate a function and its first two derivatives. We first investigate these kernels and their main properties.…”

Section: Particle Methods With Piecewise Constant Kernelsmentioning

confidence: 99%

Numerical modeling of magneto‐hydrodynamics flows using reproducing kernel particle method

Tatari

Shahriari

Raoofi

2015

Int J Numerical Modelling

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In this paper, we develop some mesh-free particle methods for magneto-hydrodynamics equations. Our focus is on the problems with high Hartmann numbers, which generate unstable solutions in most numerical methods. Several numerical tests validate the efficiency of our methods. 21. Hsieh PW, Yang SY. Two new upwind difference schemes for a coupled system of convectiondiffusion equations arising from the steady MHD duct flow problems. Journal of Computational Physics 2010; 229:9216-9234.

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Molecular dynamics simulations of mixed lubrication with smooth particle post-processing

Eder

Vernes

Vorlaufer

et al. 2011

J. Phys.: Condens. Matter

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A post-processing method for molecular dynamics (MD) simulations of friction based on the smooth particle approach is proposed, allowing--among other features--the introduction and evaluation of a solid-solid contact area arising due to direct asperity interaction. In order to illustrate the feasibility of this scheme, a large number of MD calculations of lubricated nanotribological systems with various asperity geometries and carefully selected numbers of lubricant molecules were carried out and analysed. In this manner, it is shown that the friction force as a function of load agrees very well with a three-parameter friction law which, in addition to the adhesion- and the load-controlled terms, contains a load-independent offset.

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Non-smooth kernels for meshfree methods in fluid dynamics

Cited by 3 publications

References 15 publications

A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

A stabilized meshfree reproducing kernel‐based method for convection–diffusion problems

Numerical modeling of magneto‐hydrodynamics flows using reproducing kernel particle method

Molecular dynamics simulations of mixed lubrication with smooth particle post-processing

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