Geodesic
Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 140-150 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A computational high-order algorithm for solving aerodynamics problems is presented. A direct numerical simulation method is based on the application of modern WENO-schemes at the approximation according to the space of convective summands and first derivatives of the system of full Navier–Stokes equations. Second derivatives and diffusive terms of the equations are resolved with a high-order central-difference scheme. The results of simulation with the use of the above method are demonstrated in considering the solution of two problems. It is shown that computational algorithms efficiently reproduce physical behavior of subsonic flows (vortex trail) and supersonic flows (discontinuity of parameters, air-blasts, compression shocks).
Keywords: Navier–Stocks equations, direct numerical simulation, high-order scheme, supersonic flow, Mach number. 
@article{VUU_2013_3_a10,
     author = {A. M. Lipanov and S. A. Karskanov and E. Yu. Izhboldin},
     title = {Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {140--150},
     year = {2013},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_3_a10/}
}
TY  - JOUR
AU  - A. M. Lipanov
AU  - S. A. Karskanov
AU  - E. Yu. Izhboldin
TI  - Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2013
SP  - 140
EP  - 150
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2013_3_a10/
LA  - ru
ID  - VUU_2013_3_a10
ER  - 
%0 Journal Article
%A A. M. Lipanov
%A S. A. Karskanov
%A E. Yu. Izhboldin
%T Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2013
%P 140-150
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2013_3_a10/
%G ru
%F VUU_2013_3_a10
A. M. Lipanov; S. A. Karskanov; E. Yu. Izhboldin. Solution of unsteady aerodynamics problems on the basis of the numerical algorithms of high-order approximation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 140-150. http://geodesic.mathdoc.fr/item/VUU_2013_3_a10/

[1] Kudryavtsev A. N., Poplavskaya T. V., Khotyanovskii D. V., “Application of high-order accuracy schemes to numerical simulation of unsteady supersonic flows”, Mat. Model., 19:7 (2007), 39–55 | MR | Zbl

[2] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Mathematical problems of numerical solution for hyperbolic systems of equations, Fizmatlit, Moscow, 2001 | MR

[3] Vorozhtsov E. V., “Application of Lagrange–Burman expansions for numerical integration of inviscid gas equations”, Vychislitel'nye Metody i Programmirovanie, 12 (2011), 348–361

[4] Karskanov S. A., Lipanov A. M., “On critical Reynolds numbers in plane channels with a sudden expansion at the entry”, Computational Mathematics and Mathematical Physics, 50:7 (2010), 1195–1204 | DOI | MR | Zbl

[5] Lipanov A. M., Theoretical mechanics of newtonian quality, Nauka, Moscow, 2011, 551 pp.

[6] Gaitonde D. V., Visbal M. R., “Pade-type high-order boundary filters for the Navier–Stokes equations”, AIAA J., 38:11 (2000), 2103–2112 | DOI

[7] Rizzetta D. P., Visbal M. R., Gaitonde D. P., “Large-eddy simulations of supersonic compression ramp flow by high-order method”, AIAA J., 39:12 (2001), 2283–2292 | DOI

[8] Engquist B., Loetstedt P., Sjoergreen B., “Nonlinear filters for efficient shock computation”, Mathematical computations, 52 (1989), 232–248 | DOI | MR

[9] Yee H. C., “Explicit and implicit multidimensional compact high-resolution shock-capturing methods: formulation”, J. Comp. Phys., 131:1 (1997), 216–232 | DOI | Zbl

[10] Zalesak S. T., “A Physical interpretation of the Richtmyer two-step Lax–Wendroff scheme, and its generalization to higher spatial order”, Advances in computer methods for partial differential equations, Publ. IMACS, 1984, 491–496

[11] Zalesak S. T., “Fully multidimensional flux-corrected transport algorithms for fluids”, Journal of computation physics, 31:3 (1979), 335–362 | DOI | MR | Zbl

[12] Oran E. S., Boris J. P., Numerical simulation of reactive flow, Elsevier, New York, 1987 | MR

[13] Pinchukov V. I., “On construction of monotone predictor-corrector schemes of an arbitrary order of approximation”, Mat. Model., 3:9 (1991), 95–103 | MR | Zbl

[14] Pinchukov V. I., “Nonlinear difference filters and high accuracy symmetrical schemes monotonization”, Mat. Model., 7:3 (1995), 75–86 | MR | Zbl

[15] Shu C.-W., High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD, ICASE Report No 2001-11, 2001, 16 pp.

[16] Shu C.-W., “High order ENO and WENO schemes for computational fluid dynamics, in High-order methods for computational physics”, Lecture Notes Computational Science and Engineering, 9, Springer, 1999, 439–582 | DOI | MR | Zbl

[17] Gottlieb S., Shu C.-W., “Total variation diminishing Runge–Kutta schemes”, Mathematics of computation, 67:221 (1998), 73–85 | DOI | MR | Zbl