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, firstly we show the theory of high order operational subtract that is frequently used to solve aerodynamic problems with high accurate results. Two specific operations namely the total variation diminishing (TVD) and WENO are studied because they are widely employed in aerodynamics. Consequently, the method using TVD_Radionov and WENO (second and third order operational subtracts, respectively) for solving the transfer equation is presented. Secondly, we demonstrate the result of using the two operations above in solving the transfer equation. Outputs obtained by changing input parameters compared with each other. It is found that using TVD_Radionov (second order) and WENO (third order) give results with higher accuracy compared with that of theoretical calculation, especially, in the range of monotonic values. However, there is a significant variation in values where the function has either maximum or minimum. 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. The paper presents methods for constructing monotone difference schemes of high order of approximation for the solution of linear equations of one-dimensional hyperbolic transfer and nonlinear Navier-Stokes equations. The use of such schemes is relevant for the numerical solution of problems containing gaps in the integration of the unknown functions and other features. Use a variety of difference schemes of high order of approximation type TVD and WENO for solving the transport equation and the Navier-Stokes equations. Spatial discretization term with high temporal sampling procedure and the term with the highest order

 

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