Geodesic
Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 140-150

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A computational high-order algorithm for solving aerodynamics problems is presented. A direct numerical simulation method is based on the application of modern WENO-schemes at the approximation according to the space of convective summands and first derivatives of the system of full Navier–Stokes equations. Second derivatives and diffusive terms of the equations are resolved with a high-order central-difference scheme. The results of simulation with the use of the above method are demonstrated in considering the solution of two problems. It is shown that computational algorithms efficiently reproduce physical behavior of subsonic flows (vortex trail) and supersonic flows (discontinuity of parameters, air-blasts, compression shocks).
Keywords: Navier–Stocks equations, direct numerical simulation, high-order scheme, supersonic flow, Mach number. 
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     author = {A. M. Lipanov and S. A. Karskanov and E. Yu. Izhboldin},
     title = {Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {140--150},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_3_a10/}
}
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A. M. Lipanov; S. A. Karskanov; E. Yu. Izhboldin. Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 140-150. http://geodesic.mathdoc.fr/item/VUU_2013_3_a10/