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The problem of three-dimensional mathematical modelling of the e ect of air ow 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 ow of a viscous gas is developed. The software for simulating the process of ow past a WMU model in the aircraft compartment was created. The e ect of the air ow on the OMU is described by the torque acting on the OMU from the air ow 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, modi ed for the calculation of high-speed compressible ows. To signi cantly reduce the cost of computing resources, it is suggested to use stochastic models of the e ect of air ow on WMU. A general simulation algorithm is described.

vestnik ûžno-uralʹskogo gosudarstvennogo universiteta. seriâ, matematičeskoe modelirovanie i programmirovanie

Mathematical and Software Support for 3D Mathematical Modelling of the Airflow Impact on the Optical-Mechanical Unit Mounted in the Aircraft Unpressurized Compartment