Geodesic
Heat and mass transfer in supercritical fluids on the basis of one-dimensional Navier--Stokes
Matematičeskoe modelirovanie, Tome 9 (1997) no. 12, pp. 31-42.

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The paper is devoted to a problem of numerical modelling of heat and mass transfer of a supercritical fluid close to critical point (point on a phase diagram, where properties of fluid and gas become equal), where pure fluids have strong anomalies of thermodynamic and transport properties. Modelling is made on the basis of the full 1-D Navier–Stokes equations of a viscous, compressible, conductive gas with van der Waals equation of state and prescribed dependence of thermal conductivity on temperature. An implicit noniterative algorithm based on transformation to divergent variables and use of vector Thomas algorithm is proposed. Comparisons with analytic asymptotic solutions and results of a numerical modelling based on SIMPLE method are presented. The results of numerical modelling of “critical speeding up”, “piston effect” and “acoustic saturation” phenomena in supercritical fluids are analyzed. 
@article{MM_1997_9_12_a2,
     author = {M. K. Ermakov},
     title = {Heat and mass transfer in supercritical fluids on the basis of one-dimensional {Navier--Stokes}},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {31--42},
     publisher = {mathdoc},
     volume = {9},
     number = {12},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1997_9_12_a2/}
}
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M. K. Ermakov. Heat and mass transfer in supercritical fluids on the basis of one-dimensional Navier--Stokes. Matematičeskoe modelirovanie, Tome 9 (1997) no. 12, pp. 31-42. http://geodesic.mathdoc.fr/item/MM_1997_9_12_a2/