This article is cited in 3 papers

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

A. S. Romankov^a, E. I. Romenski<sup>b

a</sup> Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
^b Sobolev Institute Mathematics of SB RAS, 4 Acad. Koptyug pr., Novosibirsk, 630090, Russia

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.

UDC: 534.18

Received: 20.05.2013
Revised: 20.08.2013

 English version: Numerical Analysis and Applications, 2014, 7:3, 215–226

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