Geodesic
Through marching method of calculation of transonic viscous flows
Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 3-22.

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The stationary problems of transonic gas dynamics – direct problem of Laval nozzle and problem of a supersonic flow over the smooth blunt-shaped body – are considered within the framework of elliptichyperbolic simplification of the Navier–Stokes equations. For the solution of these problems the fast converging iterative algorithm based on splitting, offered earlier by the author, of a gradient of pressure in a main direction of flow into “hyperbolic” and “elliptic” components is advanced. Last component in the beginning of each iteration of algorithm is fixed, and in the end – is specified. Thus the type of system of the governing equations becomes hyperbolic-parabolic. For the given system of the equations the correct mathematical problem for a finding of the unique solution describing smooth, subsonic and supersonic mixed flow or in a nozzle or in a shock layer about a blunt-shaped body is formulated. The high-resolution space-marching method allowing to carry out integration of this system of the equations through all area of flow including its transonic part is developed. Thus the difference scheme, approximating system of the differential equations, is completely implicit, uniform scheme. The effective computing condition, permitting fast to find critical values of governing parameters of the specified mixed flows is offered. 
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B. V. Rogov. Through marching method of calculation of transonic viscous flows. Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 3-22. http://geodesic.mathdoc.fr/item/MM_2004_16_5_a0/

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