Geodesic
A second-order monotone difference scheme for hyperbolic systems with two independent variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 4, pp. 848-859

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Considering the example of the equations of one-dimensional non-stationary gas dynamics, a modification of Godunov's well-know scheme is proposed for hyperbolic systems with two independent variables; the modification, while preserving the monotonicity, raises to second order the approximation of the differential operator and reduces smearing of contact discontinuities and low-intensity jumps. 
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     author = {V. I. Kopchenov and A. N. Kraiko},
     title = {A second-order monotone difference scheme for hyperbolic systems with two independent variables},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {848--859},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_4_a7/}
}
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V. I. Kopchenov; A. N. Kraiko. A second-order monotone difference scheme for hyperbolic systems with two independent variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 4, pp. 848-859. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_4_a7/