I.V. Egorov - Dr. Sc. (Phys.-Math.), Professor, Lecturer, Moscow Institute of Physics and Technology (State University); Head of Department, Central Aerohydrodynamic Institute (Moscow). E-mail: ivan.egorov@tsagi.ru Q.H. Dinh - Post-graduate Student, Moscow Institute of Physics and Technology (State University). E-mail: hoangquan10383@gmail.com

In this work, we show how to solve a complete problem starting with choosing operational subtract, doing simulation and verifying result. Application of calculation method in simulation of flows surrounding aircrafts flying with supersonic speed is always emergency and significant in aerodynamics. In the first part of this paper, we present fundamental theory of the calculation method and its application in a specific problem: flows on a thin flat surface. From the original Navier-Stokes system equations applying for viscous flows, we use approximately method to transform the Navier equations to simpler ones. From that, their solutions is simulated by using general subtract operations. Subsequently, TVD and WENO are used to solve the above problem. In the next part of this work, we present simulation result of flows on a thin flat surface by changing the input parameters using the method shown previously. Simulation of pressure, speed and temperature on the thin surface is demonstrated. The simulation result is highly consistent with experimental data. The simulation results changed accordingly with the input parameters and well agreement with theory. Finally, the two operations are applied for solving Navier_Stokes equation with flows having speech Mach = 5 and coefficient of Reynold = 105. This is a directly simulation method DNS based on solving the Navier_Stokes equation. Currently, this approach is advantageous because of high accurate result. However, the drawback of this technique is that it is required powerful computer systems. In order to find the best operation between the two, we changed the input parameters and compared the output of profile pressure, speed, temperature obtained by using TVD (second order) and WENO (third order). It is suggested that the WENO is more advanced compared with TVD. For the simulation of hypersonic flow over the plate software package High Speed Flow (HSFlow) solver was used, developed in TsAGI, allowing solving the Navier-Stokes and Reynolds equations. Use of this package allowed us to obtain a flow field on the plate and to compare them with the results obtained in wind tunnels

 

1. Godunov S.K. CHislennoe reshenie mnogomernykh zadach gazovojj dinamiki. M.: Nauka. 1976.
2. Godunov S.K. Konechno-raznostnyjj metod chislennogo rascheta razryvnykh reshenijj uravnenijj gazovojj dinamiki // Matematicheskijj sbornik. 1959. T. 47. S. 271−291.
3. Godunov S.K., Zabrodin A.V., Ivanov M.JA.,Krajjko A.N., Prokopov G.P. CHislennoe reshenie mnogomernykh zadach gazovojj dinamiki // Mat. sb. 1976. T. 47. S. 271−291.
4. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference scheme // J. Comput. Phys. 1981. V. 43. P. 357−372.
5. Bashkin V.A., Egorov I.V., Ivanov D.V. Primenenie metoda Njutona k raschetu vnutrennikh sverkhzvukovykh otryvnykh techenijj // PMTF. 1997. № 1. S. 30−42.