Solution of the nonlinear equation for isothermal gas flows in porous medium by Trefftz method
Keywords:
isothermal gas flow, porous medium, Trefftz method, fundamental solutionAbstract
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.
References
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[2] K. Balakrishnan, A. Ramachandran. A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer. Jour'nal 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. Compnters and Mathematics with Applications, 43: 289- 304, 2002.
[4] C.S. Chen. The method of fundamental solutions for non-linear thermal explosions. Communications in Nnmerical 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.
[2] K. Balakrishnan, A. Ramachandran. A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer. Jour'nal 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. Compnters and Mathematics with Applications, 43: 289- 304, 2002.
[4] C.S. Chen. The method of fundamental solutions for non-linear thermal explosions. Communications in Nnmerical 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.
Published
2022-11-17
Issue
pp. 445-456
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Uściłowska, A., & Kołodziej, J. A. (2022). Solution of the nonlinear equation for isothermal gas flows in porous medium by Trefftz method. Computer Assisted Methods in Engineering and Science, 13(3), 445-456. https://cames3.ippt.pan.pl/index.php/cames/article/view/945
