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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2014, Volume 17, Number 3, Pages 259–271 (Mi sjvm547)  
This article is cited in 2 scientific papers (total in 2 papers)

The Runge–Kutta/WENO method for solving equations for small-amplitude wave propagation in a saturated porous medium

A. S. Romankova, E. I. Romenskib

a Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
b Sobolev Institute Mathematics of SB RAS, 4 Acad. Koptyug pr., Novosibirsk, 630090, Russia
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Abstract: A high-accuracy Runge–Kutta/WENO method up to fourth order with respect to time and fifth order with respect to space is developed for the numerical modeling of the small-amplitude wave propagation in a steady fluid-saturated porous medium. The system of governing equations is derived from the general thermodynamically compatible model of a compressible fluid flow through a saturated elastic porous medium, which is described by the hyperbolic system of conservation laws with allowance for finite deformations of the medium. The results of numerical solution of one- and two-dimensional wavefields demonstrate efficiency of the method developed.
Key words: high-accuracy methods, hyperbolic system of conservation laws, saturated elastic porous media, wave propagation.
Received: 20.05.2013
Revised: 20.08.2013
English version:
Numerical Analysis and Applications, 2014, Volume 7, Issue 3, Pages 215–226
DOI: https://doi.org/10.1134/S1995423914030045
Bibliographic databases:
Document Type: Article
UDC: 534.18
Language: Russian
Citation: A. S. Romankov, E. I. Romenski, “The Runge–Kutta/WENO method for solving equations for small-amplitude wave propagation in a saturated porous medium”, Sib. Zh. Vychisl. Mat., 17:3 (2014), 259–271; Num. Anal. Appl., 7:3 (2014), 215–226
Citation in format AMSBIB
\Bibitem{RomRom14}
\by A.~S.~Romankov, E.~I.~Romenski
\paper The Runge--Kutta/WENO method for solving equations for small-amplitude wave propagation in a~saturated porous medium
\jour Sib. Zh. Vychisl. Mat.
\yr 2014
\vol 17
\issue 3
\pages 259--271
\mathnet{http://mi.mathnet.ru/sjvm547}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3409485}
\transl
\jour Num. Anal. Appl.
\yr 2014
\vol 7
\issue 3
\pages 215--226
\crossref{https://doi.org/10.1134/S1995423914030045}
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