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Acta Mechanica Sinica
Erschienen in: Acta Mechanica Sinica 3/2018

19.01.2018 | Research Paper

Enriched reproducing kernel particle method for fractional advection–diffusion equation

verfasst von: Yuping Ying, Yanping Lian, Shaoqiang Tang, Wing Kam Liu

Erschienen in: Acta Mechanica Sinica | Ausgabe 3/2018

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Abstract

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection–diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.
Vorheriger Artikel A prediction model for the effective thermal conductivity of nanofluids considering agglomeration and the radial distribution function of nanoparticles
Nächster Artikel Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

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Literatur
1.
Chen, J.S., Pan, C., Roque, C.M.O.L., et al.: A Lagrangian reproducing kernel particle method for metal forming analysis. Comput. Mech. 22, 289–307 (1998)CrossRefMATH
2.
Chen, J.S., Pan, C., Wu, C., et al.: Reproducing kernel particle methods for large deformation analysis of non-linear structures. Comput. Methods Appl. Mech. 139, 195–227 (1996)MathSciNetCrossRefMATH
3.
Chen, J.S., Pan, C., Wu, C.: Large deformation analysis of rubber based on a reproducing kernel particle method. Comput. Mech. 19, 211–227 (1997)MathSciNetCrossRefMATH
4.
Lian, Y., Zhang, X., Liu, Y.: An adaptive finite element material point method and its application in extreme deformation problems. Comput. Methods Appl. Mech. 241, 275–285 (2012)CrossRefMATH
5.
Belytschko, T., Lu, Y., Gu, L.: Crack propagation by element-free Galerkin methods. Eng. Fract. Mech. 51, 295–315 (1995)CrossRef
6.
Belytschko, T., Tabbara, M.: Dynamic fracture using element-free Galerkin methods. Int. J. Numer. Mech. Eng. 39, 923–938 (1996)CrossRefMATH
7.
Guan, P.C., Chi, S.W., Chen, J.S., et al.: Semi-Lagrangian reproducing kernel particle method for fragment-impact problems. Int. J. Impact Eng. 38, 1033–1047 (2011)CrossRef
8.
Chi, S., Lee, C., Chen, J.S., et al.: A level set enhanced natural kernel contact algorithm for impact and penetration modeling. Int. J. Numer. Mech. Eng. 102, 839–866 (2015)MathSciNetCrossRefMATH
9.
Liu, W.K., Chen, Y.: Wavelet and multiple scale reproducing kernel methods. Int. J. Numer. Methods Fluids 21, 901–931 (1995)MathSciNetCrossRefMATH
10.
Li, S., Liu, W.K.: Moving least-square reproducing kernel method part II: Fourier analysis. Comput. Methods Appl. Mech. 139, 159–193 (1996)MathSciNetCrossRefMATH
11.
Liu, W.K., Jun, S., Li, S., et al.: Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Mech. Eng. 38, 1655–1679 (1995)MathSciNetCrossRefMATH
12.
13.
Liu, W.K., Chen, Y., Jun, S., et al.: Overview and applications of the reproducing kernel particle methods. Arch. Comput. Methods Eng. 3, 3–80 (1996)MathSciNetCrossRef
14.
Bessa, M.A., Foster, J.T., Belytschko, T., et al.: A meshfree unification: reproducing kernel peridynamics. Comput. Mech. 53, 1251–1264 (2014)MathSciNetCrossRefMATH
15.
Carpinteri, A., Mainardi, F.: Fractals and Fractional Calculus in Continuum Mechanics. Springer, Vienna (1997)CrossRefMATH
16.
Metzler, R., Klafter, J.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)MathSciNetCrossRefMATH
17.
Benson, D.A., Wheatcraft, S.W., Meerschaert, M.M.: Application of a fractional advection–dispersion equation. Water Resour. Res. 36, 1403–1412 (2000)CrossRef
18.
Chen, W., Sun, H., Zhang, X., et al.: Anomalous diffusion modeling by fractal and fractional derivatives. Comput. Math. Appl. 59, 1754–1758 (2010)MathSciNetCrossRefMATH
19.
West, B.J.: Colloquium: fractional calculus view of complexity: a tutorial. Rev. Mod. Phys. 86, 1169 (2014)CrossRef
20.
Chen, W., Liang, Y., Hu, S.: Fractional derivative anomalous diffusion equation modeling prime number distribution. Fract. Calc. Appl. Anal. 18, 789–798 (2015)MathSciNetCrossRefMATH
21.
Lei, D., Liang, Y., Xiao, R.: A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics. Physica A 450, 465–475 (2018)MathSciNetCrossRef
22.
Xiao, R., Sun, H., Chen, W.: A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers. Int. J. Nonlinear Mech. 93, 7–14 (2017)CrossRef
23.
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic press, New York (1998)MATH
24.
Li, C., Zeng, F.: Numerical Methods for Fractional Calculus. CRC Press, Boca Raton (2015)MATH
25.
26.
Pang, G., Chen, W., Sze, K.Y.: A comparative study of finite element and finite difference methods for two-dimensional space-fractional advection–dispersion equation. Adv. Appl. Math. Mech. 8, 166–186 (2016)MathSciNetCrossRef
27.
Ding, H., Li, C., Chen, Y.: High-order algorithms for Riesz derivative and their applications (II). J. Comput. Phys. 293, 218–237 (2015)MathSciNetCrossRefMATH
28.
Ying, Y., Lian, Y., Tang, S., et al.: High-order central difference scheme for Caputo fractional derivative. Comput. Methods Appl. Mech. 317, 42–54 (2017)MathSciNetCrossRef
29.
Ervin, V.J., Roop, J.P.: Variational solution of fractional advection dispersion equations on bounded domains in \({\mathbb{R}}^{d}\). Numer. Methods Parial Differ. Equ. 23, 256–281 (2007)CrossRefMATH
30.
Fix, G.J., Roof, J.P.: Least squares finite-element solution of a fractional order two-point boundary value problem. Comput. Math. Appl. 48, 1017–1033 (2004)MathSciNetCrossRefMATH
31.
Ervin, V.J., Roop, J.P.: Variational formulation for the stationary fractional advection dispersion equation. Numer. Methods Partial Differ. Equ. 22, 558–576 (2006)MathSciNetCrossRefMATH
32.
Lian, Y., Ying, Y., Tang, S., et al.: A Petrov–Galerkin finite element method for the fractional advection–diffusion equation. Comput. Methods Appl. Mech. 309, 388–410 (2016)MathSciNetCrossRef
33.
Luan, S., Lian, Y., Ying, Y., et al.: An enriched finite element method to fractional advection–diffusion equation. Comput. Mech. 60, 181–201 (2017)MathSciNetCrossRefMATH
34.
Zayernouri, M., Karniadakis, G.E.: Fractional Sturm–Liouville eigen-problems: theory and numerical approximation. J. Comput. Phys. 252, 495–517 (2013)MathSciNetCrossRefMATH
35.
Zayernouri, M., Karniadakis, G.E.: Exponentially accurate spectral and spectral element methods for fractional ODEs. J. Comput. Phys. 257, 460–480 (2014)MathSciNetCrossRefMATH
36.
Zayernouri, M., Karniadakis, G.E.: Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. J. Comput. Phys. 293, 312–338 (2015)MathSciNetCrossRefMATH
37.
Kharazmi, E., Zayernouri, M., Karniadakis, G.E.: Petrov–Galerkin and spectral collocation methods for distributed order differential equations. SIAM J. Sci. Comput. 39, A1003–A1037 (2017)MathSciNetCrossRefMATH
38.
Fleming, M., Chu, Y.A., Moran, B., et al.: Enriched element-free Galerkin methods for crack tip fields. Int. J. Numer. Mech. Eng. 40, 1483–1504 (1997)MathSciNetCrossRef
39.
Liu, W.K., Li, S., Belytschko, T.: Moving least-square reproducing kernel methods (I): methodology and convergence. Comput. Methods Appl. Mech. 143, 113–154 (1997)MathSciNetCrossRefMATH
Metadaten
Titel
Enriched reproducing kernel particle method for fractional advection–diffusion equation
verfasst von
Yuping Ying
Yanping Lian
Shaoqiang Tang
Wing Kam Liu
Publikationsdatum
19.01.2018
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 3/2018
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-017-0742-z

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