Geodesic
The Runge--Kutta/WENO method for solving equations for small-amplitude wave propagation in a~saturated porous medium
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 3, pp. 259-271

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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. 
@article{SJVM_2014_17_3_a3,
     author = {A. S. Romankov and E. I. Romenski},
     title = {The {Runge--Kutta/WENO} method for solving equations for small-amplitude wave propagation in a~saturated porous medium},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {259--271},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2014_17_3_a3/}
}
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A. S. Romankov; E. I. Romenski. The Runge--Kutta/WENO method for solving equations for small-amplitude wave propagation in a~saturated porous medium. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 3, pp. 259-271. http://geodesic.mathdoc.fr/item/SJVM_2014_17_3_a3/