Geodesic
One-velocity model of a heterogeneous medium with a hyperbolic adiabatic kernel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 1111-1125

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The one-velocity model equations for a heterogeneous medium are presented that take into account the internal forces of interfractional interactions and heat and mass exchange. The shock adiabat obtained for the mixture agrees with the one-velocity model equations. For one-dimensional unsteady adiabatic flows, the characteristic equations are found and relations along characteristic directions are determined. It is shown that the model equations with allowance for interfractional interaction forces are hyperbolic. Several finite-difference and finite-volume schemes designed for integrating the model equations are discussed. 
@article{ZVMMF_2008_48_6_a13,
     author = {V. S. Surov},
     title = {One-velocity model of a~heterogeneous medium with a~hyperbolic adiabatic kernel},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1111--1125},
     publisher = {mathdoc},
     volume = {48},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a13/}
}
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V. S. Surov. One-velocity model of a heterogeneous medium with a hyperbolic adiabatic kernel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 1111-1125. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a13/