Mesh-free methods and time integrations for transient heat conduction

V. Sladek; J. Sladek; C. Zhang

V. Sladek Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava
J. Sladek Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava
C. Zhang Department of Civil Engineering, University of Siegen, Siegen

Abstract

The paper deals with transient heat conduction in functionally gradient materials. The spatial variation of the temperature field is approximated by using alternatively two various mesh free approximations, while the time dependence is treated either by the Laplace transform method and/or by the polynomial interpolation in the time stepping method. The accuracy and convergence of the numerical results as well as the computational efficiency of various approaches are compared in numerical test example.

Keywords

heat transfer, boundary value problems, numerical analysis, integral equations, meshless methods,

References

[1] P. Lancaster, K. Salkauskas. Surfaces generated by moving least square methods. Math. Comput., 37: 141–158, 1981.
[2] G.R. Liu. Mesh Free Methods, Moving Beyond the Finite Element Method. CRC Press, Boca Raton, 2003.
[3] V. Sladek, J. Sladek, M. Tanaka, Ch. Zhang. Transient heat conduction in anisotropic and functionally graded media by local integral equations. Eng. Anal. Bound. Elem., 29: 1047–1065, 2005.
[4] V. Sladek, J. Sladek, Ch. Zhang. Analytical integrations in meshless implementations of local integral equations. In: B.A. Schrefler, U. Perego [Eds.], WCCM 8: Proceedings of the 8th World Congress on Computational Mechanics, CD-ROM, ISBN 978-84-96736-55-9. CIMNE, Barcelona, 2008.
[5] V. Sladek, J. Sladek, Ch. Zhang. Computation of stresses in non-homogeneous elastic solids by local integral equation method: a comparative study. Comput. Mech., 41: 827–845, 2008.
[6] V. Sladek, J. Sladek, Ch. Zhang. Meshless implementations of local integral equations. In: C.A. Brebbia [Ed.], BEM/MRM 31: Mesh Reduction Methods, 71–82. WIT Press, Southampton, 2009.
[7] V. Sladek, J. Sladek. Local integral equations implemented by MLS-approximation and analytical integrations. Eng. Anal. Bound. Elem., 34: 904–913, 2010.
[8] H. Stehfest. Algorithm 368: Numerical Inversion of Laplace transform. Commun. Assoc. Comp. Machinery, 13: 47–49, 624, 1970.
[9] P.H. Wen, M.H. Aliabadi. An improved meshless collocation method for elastostatic and elastodynamic problems. Commun. Numer. Meth. Engng., 24: 635–651, 2008.
[10] L.C. Wrobel. The Boundary Element Method, Vol. 1: Applications in Thermo-Fluids and Acoustics. Wiley, Chichester, 2002.