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Solution of the nonlinear equation for isothermal gas flows in porous medium by Trefftz method

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents numerical solution to a problem of the transient flow of gas within a two-dimensional porous medium. A method of fundamental solution for space variables and finite difference method for time variable are employed to obtain a solution of the non-linear partial differential equation describing the flow of gas. The inhomogeneous term is expressed by radial basis functions at each time steps. Picard iteration is used for treating nonlinearity.
Rocznik
Strony
445--456
Opis fizyczny
Bibliogr. 11 poz., rys.
Twórcy
  • Poznań University of Technology, Institute of Applied Mechanics [Politechnika Poznańska], ul. Piotrowo 3, 60-965 Poznań
Bibliografia
  • [1] M.R. Akella, G.R. Katamraju. Trefftz indirect method applied to nonlinear potential problems. Engineering Analysis with Boundary Elements, 24: 459-465, 2000.
  • [2] K. Balakrishnan, A. Ramachandran. A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer. Journal of Computational Physics, 150: 239-267, 1999.
  • [3] K. Balakrishnan, R. Sureshkumar, A. Ramachandran. An operator splitting-radial basis functions method for the solution of transient nonlinear Poisson problems. Computers and Mathematics with Applications, 43: 289-304, 2002.
  • [4] C.S. Chen. The method of fundamental solutions for non-linear thermal explosions. Communications in Numerical Methods in Engineering, 11: 675-681, 1995.
  • [5] A. Karageorghis, G. Fairweather. The method of fundamental solutions for the solutions of nonlinear plane potential problems. IMA Journal of Numerical Analysis. 9: 231-242, 1989.
  • [6] R.E. Kidder. Unsteady flow of gas through a semi-infinite porous medium. Journal of Applied Mechanics, 79: 329-334, 1957.
  • [7] E. Kita, Y. Ikeda, N. Kamyia. Application of Trefftz method to steady-state heat conduction problem in functionally gradient materials. Computer Assisted Mechanics and Engineering Sciences, 10: 339-351, 2003.
  • [8] T. Klekiel, J.A. Kołodziej. Application of radial basis function for solution nonlinear heat conduction problem using evolutionary algorithm. In: B.T. Maruszewski, W. Muschik, A. Rodowicz (eds.), Proceedings of the. International Symposium on Trends in Continuum Physics. Poznań University of Technology, 176-186. 2004.
  • [9] A.S. Muleshkov, M.A. Goldberg, C.S. Chen. Particular solutions of Helmholtz-type operators using higher order polyharmonic splines. Computational Mechanics, 23: 411-419, 1999.
  • [10] M.M. Rienecker, J.D. Fenton. Fourier approximation method for steady water waves. Journal of Fluid Mechanics, 104: 119-137, 1981.
  • [11] A. Uściłowska-Gajda, J.A. Kołodziej, M. Ciałkowski, A. Frąckowiak. Comparison of two types of Trefftz method for the solution of inhomogeneous elliptic problems. Computer Assisted Mechanics and Engineering Sciences, 10: 661-675, 2003.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0025-0007
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