Abstract
The algorithm for numerical solving the Navier-Stokes equations for two-dimensional motion for viscous heat-conducting gas is proposed. The discretization of equations is performed by a combination of a special version of the trajectory method for a substantial derivative and the finite element method with piecewise bilinear basis functions for other terms. The results of numerical studies of the structure of a supersonic flow in a plane channel with an obstacle for a wide range of Mach numbers and Reynolds numbers are presented. Velocity and pressure fields are investigated, and the vortex structure of flow is studied in the circulation area of the obstacle.
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References
ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. Notes on Numerical Fluid Mechanics and Multidisciplinary Design vol. 113. Springer (2010)
Oberkampf, W.L., Trucano, T.G.: Verification and validation in computational fluid dynamics. Progress in Aerospace Sciences 38, 209–272 (2002)
Shaidurov, V.V., Shchepanovskaya, G.I., Yakubovich, M.V.: Application of the trajectories and finite element method in modeling the motion of a viscous heat-conducting gas. Computational Methods and Programming 12, 275–281 (2011)
Bosnyakov, S., Kursakov, I., Lysenkov, A., Matyash, S., Mikhailov, S., Vlasenko, V., Quest, J.: Computational tools for supporting the testing of civil aircraft configurations in wind tunnels. Progress in Aerospace Sciences 44, 67–120 (2008)
Vos, J.B., Rizzi, A., Darracq, D., Hirschel, E.H.: Navier-Stokes solvers in European aircraft design. Progress in Aerospace Sciences 38, 601–697 (2002)
The Handbook of Fluid Dynamics. CRC Press LLC & Springer (1998)
Pironneau, O.: On the Transport-Diffusion Algorithm and Its Applications to the Navier-Stokes Equations. Numerische Mathematik 38, 309–332 (1982)
Chen, H., Lin, Q., Shaidurov, V.V., Zhou, J.: Error Estimates for Trangular and Tetrahedral Finite Elements in Combination with a Trajectory Approximation of the First Derivatives for Advection-Diffusion Equations. Numerical Analysis and Applications 4(4), 345–362 (2011)
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Shaydurov, V.V., Shchepanovskaya, G.I., Yakubovich, M.V. (2013). Some New Approaches to Solving Navier-Stokes Equations for Viscous Heat-Conducting Gas. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_11
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DOI: https://doi.org/10.1007/978-3-642-41515-9_11
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