Received:

Revised:

Accepted:

Published online:

DOI:
10.5802/crmeca.49

Revised:

Accepted:

Published online:

Keywords:
Radial point interpolation method (RPIM), Homotopy transformation, High-order continuation, Heat conduction, Thermal conductivity

Author's affiliations:

Said Mesmoudi ^{1};
Omar Askour ^{1};
Bouazza Braikat ^{1}

License: CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRMECA_2020__348_8-9_745_0, author = {Said Mesmoudi and Omar Askour and Bouazza Braikat}, title = {Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems}, journal = {Comptes Rendus. M\'ecanique}, pages = {745--758}, publisher = {Acad\'emie des sciences, Paris}, volume = {348}, number = {8-9}, year = {2020}, doi = {10.5802/crmeca.49}, language = {en}, }

TY - JOUR AU - Said Mesmoudi AU - Omar Askour AU - Bouazza Braikat TI - Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems JO - Comptes Rendus. Mécanique PY - 2020 SP - 745 EP - 758 VL - 348 IS - 8-9 PB - Académie des sciences, Paris DO - 10.5802/crmeca.49 LA - en ID - CRMECA_2020__348_8-9_745_0 ER -

%0 Journal Article %A Said Mesmoudi %A Omar Askour %A Bouazza Braikat %T Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems %J Comptes Rendus. Mécanique %D 2020 %P 745-758 %V 348 %N 8-9 %I Académie des sciences, Paris %R 10.5802/crmeca.49 %G en %F CRMECA_2020__348_8-9_745_0

Said Mesmoudi; Omar Askour; Bouazza Braikat. Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems. Comptes Rendus. Mécanique, Volume 348 (2020) no. 8-9, pp. 745-758. doi : 10.5802/crmeca.49. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.49/

[1] Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method, Appl. Math. Modelling, Volume 35 (2011) no. 9, pp. 4157-4174 | DOI | MR | Zbl

[2] A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems, Int. J. Heat Mass Transfer, Volume 84 (2015), pp. 729-739 | DOI

[3] Temperature-dependent conductivity in forced convection of heat exchangers filled with porous media: a perturbation solution, Energy Convers. Manage., Volume 91 (2015), pp. 259-266 | DOI

[4] Radial integration BEM for solving transient nonlinear heat conduction with temperature-dependent conductivity, Int. J. Heat Mass Transfer, Volume 108 (2017), pp. 1551-1559 | DOI

[5] RIBEM for 2D and 3D nonlinear heat conduction with temperature dependent conductivity, Eng. Anal. Bound. Elem., Volume 87 (2018), pp. 1-8 | DOI | MR | Zbl

[6] Homotopy method of fundamental solutions for solving nonlinear heat conduction problems, Eng. Anal. Bound. Elem., Volume 108 (2019), pp. 179-191 | DOI | MR

[7] Implementation of a standard stream-upwind stabilization scheme in the element-free Galerkin based solution of advection-dominated heat transfer problems during solidification in direct chill casting processes, Eng. Anal. Bound. Elem., Volume 106 (2019), pp. 170-181 | DOI | MR | Zbl

[8] Surfaces generated by moving least squares methods, Math. Comput., Volume 155 (1981), pp. 141-158 | DOI | MR | Zbl

[9] A point interpolation method for two-dimensional solids, Int. J. Numer. Methods Eng., Volume 50 (2001) no. 4, pp. 937-951 | DOI | Zbl

[10] A point interpolation meshless method based on radial basis functions, Int. J. Numer. Methods Eng., Volume 54 (2002) no. 11, pp. 1623-1648 | DOI | Zbl

[11] An Introduction to Meshfree Methods and their Programming, Springer Science & Business Media, 2005

[12] Meshless methods: a review and computer implementation aspects, Math. Comput. Simul., Volume 79 (2008) no. 3, pp. 763-813 | DOI | MR | Zbl

[13] Natural convection heat transfer at high Rayleigh numbers-extended meshless local Petrov-Galerkin (MLPG) primitive variable method, Eng. Anal. Bound. Elem., Volume 44 (2014), pp. 170-184 | DOI | MR | Zbl

[14] A novel approach to impose periodic boundary condition on braided composite RVE model based on RPIM, Compos. Struct., Volume 163 (2017), pp. 77-88 | DOI

[15] A Cell-based Smoothed Radial Point Interpolation Method (CS-RPIM) for heat transfer analysis, Eng. Anal. Bound. Elem., Volume 40 (2014), pp. 147-153 | DOI | MR | Zbl

[16] Dynamic analysis of a thin-walled beam with open cross section subjected to dynamic loads using a high-order implicit algorithm, Eng. Struct., Volume 120 (2016), pp. 133-146 | DOI

[17] From homotopy perturbation technique to reduced order model for multiparametric modal analysis of large finite element models, Mech. Syst. Signal Process., Volume 96 (2017), pp. 291-302 | DOI

[18] Numerical comparisons of high-order nonlinear solvers for the transient navier-stokes equations based on homotopy and perturbation techniques, J. Comput. Appl. Math., Volume 289 (2015), pp. 356-370 | DOI | MR | Zbl

[19] Study of damped vibrations of a vibroacoustic interior problem with viscoelastic sandwich structure using a High Order Newton solver, J. Sound Vib., Volume 462 (2019), 114947 | DOI

[20] An implicit algorithm based on continuous moving least square to simulate material mixing in friction stir welding process, Modelling Simul. Eng., Volume 2013 (2013), pp. 1-14 | DOI

[21] A new algorithm based on moving least square method to simulate material mixing in friction stir welding, Eng. Anal. Bound. Elem., Volume 50 (2015), pp. 372-380 | DOI

[22] A numerical mesh-free model for elasto-plastic contact problems, Eng. Anal. Bound. Elem., Volume 82 (2017), pp. 68-78 | DOI | MR | Zbl

[23] A 2D mechanical-thermal coupled model to simulate material mixing observed in friction stir welding process, Eng. Comput., Volume 33 (2017) no. 4, pp. 885-895 | DOI

[24] High order mesh-free method for frictional contact, Eng. Anal. Bound. Elem., Volume 94 (2018), pp. 103-112 | DOI | MR | Zbl

[25] A high order mesh-free method for buckling and post-buckling analysis of shells, Eng. Anal. Bound. Elem., Volume 99 (2019), pp. 89-99 | DOI | MR | Zbl

[26] Solving the incompressible fluid flows by a high-order mesh-free approach, Int. J. Numer. Methods Fluids, Volume 92 (2020) no. 5, pp. 422-435 | DOI | MR

[27] Three-dimensional numerical simulation of material mixing observed in FSW using a mesh-free approach, Eng. Comput., Volume 36 (2020), pp. 13-27 | DOI

[28] Numerical analysis of single-layered graphene sheets by a mesh-free approach, Eng. Comput. (2020), pp. 1-14 (in press)

[29] On the use of Radial Point Interpolation Method (RPIM) in a high order continuation for the resolution of the geometrically nonlinear elasticity problems, Eng. Anal. Bound. Elem., Volume 110 (2020), pp. 69-79 | DOI | MR | Zbl

[30] A dual-reciprocity boundary element approach for axisymmetric nonlinear time-dependent heat conduction in a nonhomogeneous solid, Eng. Anal. Bound. Elem., Volume 34 (2010) no. 8, pp. 697-706 | DOI | MR | Zbl

[31] Generalized finite difference method for solving the double-diffusive natural convection in fluid-saturated porous media, Eng. Anal. Bound. Elem., Volume 95 (2018), pp. 175-186 | MR | Zbl

[32] The determination temperature-dependent thermal conductivity as inverse steady heat conduction problem, Int. J. Heat Mass Transfer, Volume 54 (2011) no. 4, pp. 790-796 | DOI | Zbl

[33] The singular boundary method for steady-state nonlinear heat conduction problem with temperature-dependent thermal conductivity, Int. J. Heat Mass Transfer, Volume 91 (2015), pp. 205-217 | DOI

[34] A new modified Levenberg–Marquardt algorithm for identifying the temperature-dependent conductivity of solids based on the radial integration boundary element method, Int. J. Heat Mass Transfer, Volume 144 (2019), 118615 | DOI

[35] Meshless local B-spline collocation method for heterogeneous heat conduction problems, Eng. Anal. Bound. Elem., Volume 101 (2019), pp. 76-88 | DOI | MR | Zbl

[36] Nonlinear flexural analysis of laminated composite plates using RBF based meshless method, Compos. Struct., Volume 94 (2012) no. 5, pp. 1714-1720 | DOI

[37] Nonlinear flexural analysis of functionally graded plates under different loadings using RBF based meshless method, Eng. Anal. Bound. Elem., Volume 36 (2012) no. 12, pp. 1819-1827 | DOI | Zbl

[38] RBF-based meshless Local Petrov Galerkin Method for the multi-dimensional convection–diffusion-reaction equation, Eng. Anal. Bound. Elem., Volume 98 (2019), pp. 46-53 | DOI | MR | Zbl

[39] A path-following technique via an asymptotic-numerical method, Comput. Struct., Volume 53 (1994), pp. 1181-1192 | DOI | Zbl

[40] Radial integration boundary element method for nonlinear heat conduction problems with temperature-dependent conductivity, Int. J. Heat Mass Transfer, Volume 104 (2017), pp. 1145-1151 | DOI

[41] Application of the meshless generalized finite difference method to inverse heat source problems, Int. J. Heat Mass Transfer, Volume 108 (2017), pp. 721-729 | DOI

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