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.
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