Geodesic
Mathematical and software support for 3D mathematical modelling of the airflow impact
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 113-123

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The problem of three-dimensional mathematical modelling of the effect of air flow on an optical-mechanical unit (OMU) located in the unpressurised compartment of the aircraft, is considered. To solve this problem, a mathematical model of gas dynamics based on the solution of a complete system of Navier–Stokes equations that describe the dynamics of a turbulent, spatially unsteady flow of a viscous gas is developed. The software for simulating the process of flow past a WMU model in the aircraft compartment was created. The effect of the air flow on the OMU is described by the torque acting on the OMU from the airflow side. A numerical method for solving the three-dimensional gasdynamic problem is presented. The numerical method is based on the numerical high order Godunov scheme, realized on an irregular grid with arbitrary cells (tetrahedral, prismatic shape). Flows of conservative variables are calculated by solving the Riemann problem with an approximate AUSM method. The system of equations is supplemented by a two-parameter k-model of turbulence, modified for the calculation of high-speed compressible flows. To significantly reduce the cost of computing resources, it is suggested to use stochastic models of the effect of air flow on WMU. A general simulation algorithm is described.
Keywords: optical-mechanical unit; mathematical modelling; the effects of air flow. 
@article{VYURU_2017_10_4_a10,
     author = {I. E. Ivanov and I. A. Kryukov and E. V. Larina and V. L. Miroshkin},
     title = {Mathematical and software support  for {3D} mathematical modelling of the airflow impact},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {113--123},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a10/}
}
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I. E. Ivanov; I. A. Kryukov; E. V. Larina; V. L. Miroshkin. Mathematical and software support  for 3D mathematical modelling of the airflow impact. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 113-123. http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a10/