Geodesic
Method of minimum length for finding of critical parameters of mixed flows
Matematičeskoe modelirovanie, Tome 14 (2002) no. 1, pp. 87-96

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Fast iteration algorithm for finding the critical values of governing parameters is developed to solve steady problems of internal and external mixed (with subsonic and supersonic regions) flows at moderate and large Reynolds numbers. Algorithm is based on analysis of a branching of numerical integral curves of difference equations in the transonic flow region and on the use of a principle of a minimum of length of the integral curve, which corresponds to “critical” value of the governing parameter. The method of minimum length is illustrated on examples of viscous flows through a Laval nozzle and in a shock layer near a blunt body (a sphere) in a supersonic flow. The critical value of the mass flow rate through the nozzle and a value of curvature of a shock wave on a symmetry axis of the flow are determined by the given method in the first and second examples, respectively. 
@article{MM_2002_14_1_a5,
     author = {B. V. Rogov},
     title = {Method of minimum length for finding of critical parameters of mixed flows},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {87--96},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_1_a5/}
}
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B. V. Rogov. Method of minimum length for finding of critical parameters of mixed flows. Matematičeskoe modelirovanie, Tome 14 (2002) no. 1, pp. 87-96. http://geodesic.mathdoc.fr/item/MM_2002_14_1_a5/