Transient heat conduction by different versions of the Method of Fundamental Solutions – a comparison study

• Autorzy: Kołodziej J. A. J. A. , Mierzwiczak M.
• Języki publikacji: EN

Abstrakty

EN

The computational accuracy of three versions of the method of fundamental solutions (MFS) is compared. The first version of MFS is based on the Laplace transformation of the governing differential equations and of the boundary conditions. The second version of MFS is based on the fundamental solution of the governing differential equation and discretization in time. The third method approximates the temperature time derivative by finite difference scheme. As the test problems the 2D boundary-initial-value problems (2D_BIVP) in square rectangular region ? with known exact solutions are considered. Our numerical experiments show that all discussed methods achieve relatively accurate approximate solution but the third one offers less computational complexity and better efficiency.

Słowa kluczowe

EN

method of fundamental solutions; meshless method; transient heat conductiontransient heat conduction; initial-boundary volume problem; boundary collocation method

PL

metoda rozwiązań podstawowych; metoda Meshlessa; przewodzenie ciepła nieustalone; kolokacja brzegowa

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2010
• Tom: Vol. 17, no. 1
• Strony: 75--88
• Opis fizyczny: Bibliogr. 18 poz., rys., tab., wykr.

Twórcy

autor

Kołodziej J. A. J. A.

autor

Mierzwiczak M.

• Institute of Applied Mechanics, Poznan University of Technology ul. Piotrowo 3, 60-965 Poznan, Poland

Bibliografia

• [1] R. Białecki, P. Jurgaś, G. Kuhn. Dual reciprocity BEM without matrix inversion for transient heat conduction. Engineering Analysis with Boundary Elements, 26: 227-236, 2002.
• [2] G. Fairweather, A. Karageorghis. The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, 9: 69-95, 1998.
• [3] J.A. Kołodziej, J. Stefaniak, M. Kleiber. Transient heat conduction by boundary collocation methods and FEM - a comparison study. In: W. Hackbusch, ed., Numerical Techniques for Boundary Element Methods: Proceedings of the Seventh GAMM-Seminar, Kiel, January 25-27, 1991. Published in: Notes on Numerical Fluid Mechanics, 33, pp.104-115, 1992.
• [4] C.S. Chen, M.A. Golberg, Y.C. Hon. The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations. International Journal for Numerical Methods in Engineering, 43: 1421-1435, 1998.
• [5] M.A. Golberg, C.S. Chen, A.S. Muleshkov. The method of fundamental solutions for time-dependent problems, In: C.S. Chen C.A. Brebia, D.W. Pepper, eds., Boundary Element Technology XIII, pp. 377-386, WIT Press, Southampton, 1999.
• [6] E. Mahajerin, G. Burgess. A Laplace transform-based fundamental collocation method for two-dimensional transient heat flow. Applied Thermal Engineering, 23: 101-111, 2003.
• [7] G. Burgess, E. Mahajerin. Transient heat flow analysis using the fundamental collocation method. Applied Thermal Engineering, 23: 893-904, 2003.
• [8] D.L. Young, C.C. Tsai, K. Murugesan, C.M. Fan, C.W. Chen. Time-dependent fundamental solution for homogeneous diffusion problems. Engineering Analysis with Boundary Elements, 28: 1463-1473, 2004.
• [9] M.S. Ingber, C.S. Chen, J.A. Tanski. A mesh free approaches using radial basis functions and parallel domain decomposition for solving three-dimensional diffusion equations. International Journal for Numerical Methods in Engineering, 60: 2183-2201, 2004.
• [10] C.F. Dong. An extended method of time-dependent fundamental solutions for inhomogeneous heat conduction. Engineering Analysis with Boundary Elements, 33: 717-725, 2009.
• [11] S. Chantasiriwan. Methods of fundamental solutions for time-dependent heat conduction problems. International Journal for Numerical Methods in Engineering, 66: 147-165, 2006.
• [12] R.A. Schapery. Approximation methods of transform inversion for viscoelastic stress analysis. Proceedings of the Fourth US National Congress on Applied Mechanics, 2: 1075-1085, 1962.
• [13] K.E. Atkinson. The numerical evaluation of particular solution for Poisson's equation. IMA J. Numer. Anal., 5: 319-338, 1985.
• [14] H. Stehfest. Algorithm 368: Numerical Inversion of the Laplace Transformation. Communications of the ACM, 13: 47-49, 1970.
• [15] M.A. Golberg, C.S. Chen, Y.F. Rashed. The annihilator method for computing particular solutions to partial differential eqautions. Engineering Analysis with Boundary Elements, 23: 267-274, 1999.
• [16] J.A. Kołodziej, A.P. Zieliński. Boundary Collocation Techniques and their Application in Engineering. WIT Press, Southampton 2009.
• [17] B. Davies, B. Martin. Numerical inversion of Laplace Transform: a Survey and Comparison of Methods. Journal of Computational Physics, 33: 1-32, 1979.
• [18] J. Kouatchou. Comparison of time and spatial collocation methods for the heat equation. Journal of Computational and Applied Mathematics, 150: 129-141, 2003.