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Ochiai, Y.; Sladek, V.; Sladek, J.

Transient heat conduction analysis by triple-reciprocity boundary element method. (English) Zbl 1195.80030

Eng. Anal. Bound. Elem. 30, No. 3, 194-204 (2006).
Summary: The paper deals with 2D initial-boundary value problems in the linear theory of transient heat conduction. A pure boundary element formulation is developed systematically. The time-dependent fundamental solution of the diffusion operator is employed together with higher-order polyharmonic fundamental solutions. The pseudo-initial temperature and/or heat sources density are approximated by using the triple-reciprocity formulation. All the time integrations are performed analytically in the time-marching scheme with integration within one time step and constant interpolation. The spatial discretization is reduced to boundary elements and free scattering of interior nodal points without any connectivity.

Cited in 15 Documents

MSC:

80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)

Keywords:

heat conduction; boundary element method; time-marching schemes; time-dependent fundamental solution; triple-reciprocity formulation
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References:

[1] Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary element techniques: theory and applications in engineering (1984), Springer: Springer Berlin · Zbl 0556.73086
[2] Nowak, A. J.; Neves, A. C., The multiple reciprocity boundary element method (1994), CMP: CMP Southampton · Zbl 0868.73006
[3] Nowak, A. J., The multiple reciprocity method of solving transient heat conduction problems, (Brebbia, C. A.; Connors, J. J., Advances in boundary elements, vol. 2 (1989), CMP: CMP Southampton)
[4] Tanaka M, Matsumoto T, Takakuwa S. Dual reciprocity BEM based on time-stepping scheme for solution of transient heat conduction problems. In: Boundary elements XXV. Southampton: WIT Press; 2003. p. 299-308.; Tanaka M, Matsumoto T, Takakuwa S. Dual reciprocity BEM based on time-stepping scheme for solution of transient heat conduction problems. In: Boundary elements XXV. Southampton: WIT Press; 2003. p. 299-308.
[5] Sladek, J.; Sladek, V., Local boundary integral equation method for heat conduction problem in an anisotropic medium, (Herrera, C. A., Advances in computational & experimental engineering & sciences (2003), Tech Science Press: Tech Science Press Encino, CA), [CD-ROM Proc] · Zbl 1129.74346
[6] Sladek, V.; Sladek, J.; Tanaka, M., Local integral equations for transient heat conduction in functionally graded materials, Trans JASCOME J Bound Elem Methods, 21, 7-12 (2004)
[7] Ochiai, Y.; Sekia, T., Steady heat conduction analysis by improved multiple-reciprocity boundary element method, Eng Anal Bound Elem, 18, 111-117 (1996)
[8] Ochiai, Y.; Sekia, T., Steady thermal stress analysis by improved multiple-reciprocity boundary element method, J Therm Stresses, 18, 603-620 (1995)
[9] Ochiai, Y., Axisymmetric heat conduction analysis by improved multiple-reciprocity boundary element method, Heat Transfer Jpn Res, 23, 498-512 (1995)
[10] Ochiai, Y.; Kobayashi, T., Initial stress formulation for elastoplastic analysis by improved multiple-reciprocity boundary element method, Eng Anal Bound Elem, 23, 167-173 (1999) · Zbl 0940.74076
[11] Ochiai, Y., Two-dimensional unsteady heat conduction analysis with heat generation by triple-reciprocity boundary element method, Int J Numer Methods Eng, 51, 143-157 (2001) · Zbl 0985.80008
[12] Ochiai, Y.; Sekia, T., Generation of free-form surface in CAD for dies, Adv Eng Softw, 22, 113-118 (1995)
[13] Ochiai, Y., Generation method of distributed data for FEM analysis, JSME Int J, 39, 93-98 (1996)
[14] Ochiai, Y.; Yasutomi, Z., Improved method generating a free-form surface using integral equations, Comput Aided Geom Des, 17, 233-245 (2000) · Zbl 0939.68151
[15] Ochiai, Y., Multidimensional numerical integration for meshless BEM, Eng Anal Bound Elem, 27, 241-249 (2003) · Zbl 1033.65109
[16] Dyn, N., Intrepolation of scattered data by radial functions, (Chui, C. K.; Schumaker, L. L.; Utreras, F. I., Topics in multivariate approximation (1987), Academic Press: Academic Press London), 47-61 · Zbl 0628.41001
[17] Micchelli, C. A., Interpolation of scattered data, Constr Approx, 2, 12-22 (1986)
[18] Morse, P. M.; Feshbach, H., Methods of theoretical physics (1953), Mc Graw-Hill: Mc Graw-Hill New York · Zbl 0051.40603
[19] Tanaka, M.; Sladek, V.; Sladek, J., Regularization techniques applied to boundary element methods, Appl Mech Rev, 47, 457-499 (1994)
[20] Carslaw, H. S.; Jaeger, J. C., Some problem in mathematical theory of the conduction of heat, Philos Mag, 26, 473-495 (1938) · Zbl 0019.34902
[21] Bateman, H.; Erdelyi, A., Higher transcendental functions, vol. 2 (1953), Mc Graw-Hill: Mc Graw-Hill New York · Zbl 0051.30303
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