The Runge-Kutta/WENO method for solving equations for small-amplitude wave propagation in a saturated porous medium
A.S. Romankov1, E.I. Romenski2
1Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia
2Sobolev Institute Mathematics of SB RAS, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia
Keywords: методы высокого порядка точности, гиперболические системы законов сохранения, насыщенные пористые упругие среды, распространение волн, high-accuracy methods, hyperbolic system of conservation laws, saturated elastic porous media, wave propagation
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.
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