Multiresolution reproducing kernel particle method for computational fluid dynamics

Liu, Wing Kam; Jun, Sukky; Sihling, Dirk Thomas; Chen, Yi-Jung; Wei, Hao

doi:10.1002/(sici)1097-0363(199706)24:12<1391::aid-fld566>3.0.co;2-2

Cited by 113 publications

(42 citation statements)

References 16 publications

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“…For example, meshless approaches have a considerable potential to deal with general unstructured discretizations and high-order approximations, simplifying the implementation of error estimation procedures. Among the first meshless applications, error estimates based on residuals [36] and wavelets [37] can be found. More recently, enhanced, recovered, or higher-order solution fields have been employed to obtain error estimates and indicators [38][39][40][41][42].…”

Section: /26mentioning

confidence: 99%

A-posteriori error estimation for the finite point method with applications to compressible flow

et al. 2017

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Computational mechanics. Abstract. An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

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Section: /26mentioning

confidence: 99%

A-posteriori error estimation for the finite point method with applications to compressible flow

et al. 2017

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“…Liu et al [31] outlined a Petrov±Galerkin formulation for CFD, and introduced an algorithm incorporating multiple scale adaptive re®nement. Li and Liu [24] showed how RKPM can provide synchronized rates of convergence for functions and their derivatives, and used these synchronized interpolants to stabilize the pressure solution for Stokes¯ow problems.…”

Section: Multi-scale Modelling and Rkpmmentioning

confidence: 99%

Turbulence simulation and multiple scale subgrid models

Wagner

Liu

2000

Computational Mechanics

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The problem of modelling turbulence in CFD is due to the wide range of length scales present in a turbulent¯ow. The physics of these scales is examined, and the need for models of the small scale motions is made clear. A review is given of methods of turbulence modelling. These methods can be divided into two classes: Reynolds averaged Navier±Stokes (RANS) models, and large eddy simulation (LES). The Reproducing Kernel Particle method (RKPM) is then presented and proposed as a class of ®lters for LES of inhomogeneous turbulent ows. Important properties of the method are discussed, including the effectiveness of the RKPM reproduction as a low-pass ®lter. The commutation of the ®ltering operation with differentiation is demonstrated, showing that the commutation error can be made arbitrarily small. A onedimensional non-linear example problem is solved using a Galerkin method in which a bi-scale constitutive model is used for the subgrid scale terms. The extension of the method to the three-dimensional equations of¯uid dynamics is then outlined, where the method is used as a ®lter in a dynamic subgrid stress model. Emphasis is placed on the multi-scale properties of RKPM, which allow the reproduction of different scales of the solution using the same set of nodal parameters.

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“…The subject of error estimates for meshless methods and a consequent adaptive analysis is central to the effective application of meshless algorithms for practical engineering computation. In recent years, a large amount of work has been performed concerning adaptive analysis based on a posteriori error estimation for domain-type meshless methods such as the h-p meshless method [15], the GFEM [16], the EFG method [17][18][19][20], the RKPM [21][22][23][24][25], the FPM [26] and the PIM [27,28]. Significant progress has been achieved in the theory and implementation of the adaptive procedures for these meshless methods.…”

Section: Introductionmentioning

confidence: 99%

On error estimator and adaptivity in the meshless Galerkin boundary node method

2011

Comput Mech

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In this article, a simple a posteriori error estimator and an effective adaptive refinement process for the meshless Galerkin boundary node method (GBNM) are presented. The error estimator is formulated by the difference between the GBNM solution itself and its L 2 -orthogonal projection. With the help of a localization technique, the error is estimated by easily computable local error indicators and hence an adaptive algorithm for h-adaptivity is formulated. The convergence of this adaptive algorithm is verified theoretically in Sobolev spaces. Numerical examples involving potential and elasticity problems are also provided to illustrate the performance and usefulness of this adaptive meshless method.

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Multiresolution reproducing kernel particle method for computational fluid dynamics

Cited by 113 publications

References 16 publications

A-posteriori error estimation for the finite point method with applications to compressible flow

A-posteriori error estimation for the finite point method with applications to compressible flow

Turbulence simulation and multiple scale subgrid models

On error estimator and adaptivity in the meshless Galerkin boundary node method

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