K. N. Volkov

Read the full article  ';
Article in Russian

The paper deals with an approach to finite volume discretization of unsteady Navier-Stokes equations on unstructured meshes, and its advantages and development prospects are discussed. Features of inviscid and viscous flux discretization and temporal derivatives are considered. The advantages of the proposed approach include: the ability to operate on both structured and unstructured meshes; usage of high-order finite difference schemes in time and space; selection of median control volume for discretization of governing equations; application of expressions for calculation of the gradient and pseudo-laplasian making it possible to obtain more accurate results on highly stretched meshes in the boundary layer; writing of equations for the calculation of fluxes through the faces of interior and boundary control volumes in the same form, that simplify software implementation. This approach gives the possibility to implement a strategy of mesh adaptation taking into account the features of the certain flow and gives wide opportunities to parallelize computations. Possibilities of the developed approach are demonstrated on the example of the problem solution related to simulation of unsteady flows in the gas turbine engines.

Keywords: fluid dynamics, unstructured mesh, finite-difference scheme, aerofoil

 1.     Volkov K.N., Emelyanov V.N. Vychislitel'nye Tekhnologii v Zadachakh Mekhaniki Zhidkosti i Gaza [Computer Applications in Problems of Fluid Mechanics and Gas]. Moscow, FIZMATLIT Publ., 2013, 468 p.
2.     Cagnone J.S., Sermeus K., Nadarajah S.K., Laurendeau E. Implicitmultigrid schemes for challenging aerodynamic simulations onblock-structured grids. Computers and Fluids, 2011, vol. 44, no.1, pp. 314–327. doi: 10.1016/j.compfluid.2011.01.014
3.     Deng X., Mao M., Tu G., Zhang H., Zhang Y. High-order and high accurate CFD methods and their applications for complex grid problems.Communications in Computational Physics, 2012, vol.11, no. 4, pp. 1081–1102. doi: 10.4208/cicp.100510.150511s
4.     Wang Z.J., Fidkowski K., Abgrall R., Bassi F., Caraeni D., Cary A., Deconinck H., Hartmann R., Hillewaert K., Huynh H.T., Kroll N., May G., Persson P.-O., van Leer B., Visbal M. High-order CFD methods: current status and perspective. International Journal for Numerical Methods in Fluids, 2012, vol. 72, no. 8, pp. 811–845. doi: 10.1002/fld.3767
5.     Luo H., Baum J.D., Lohner R. Edge-based finite element scheme for the Euler equations. AIAA Journal, 1994, vol. 32, no. 6, pp. 1183–1190.
6.     Crumpton P.I., Moinier P., Giles M.B. An unstructured algorithm for high Reynolds number flows on highly stretched grids. Proc. 10th International Conference on Numerical Methods in Laminar and Turbulent Flow. Swansea, U.K., 1997, pp. 561–572.
7.     Brognies Z., Rajasekharan A., Farhat C. Provably stable and time-accurate extensions of Runge-Kutta schemes for CFD computations on moving grids. International Journal for Numerical Methods in Fluids, 2012, vol. 69, no. 7, pp. 1249–1270. doi: 10.1002/fld.2636
8.     Moinier P., Giles M.B. Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes. Journal of Computational Physics, 2002, vol. 178, no. 2, pp. 498–519. doi: 10.1006/jcph.2002.7038
9.     Crumpton P.I., Giles M.B. Implicit time accurate solutions on unstructured dynamic grids. International Journal for Numerical Methods in Fluids,1997, vol. 25, no. 11, pp. 1285–1300.
10.Brandt A.Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation, 1977, vol. 31, no. 138, pp. 333–390. doi: 10.1090/S0025-5718-1977-0431719-X
11.Fransson T.H., Verdon J.M. Standard configurations for unsteady flow through vibrating axial-flow turbomachine-cascades. In Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines and Propellers. Ed. H.M. Atassi.NY: Springer-Verlay, 1993, pp. 859–889. doi: 10.1007/978-1-4613-9341-2_44
12.Verdon J.M.Linearized unsteady aerodynamic theory. United Technologies Research Center Report R85-151774-1, 1987.
13.Lawrence C., Spyropoulos E., Reddy T.S.R. Unsteady cascade aerodynamic response using a multiphysics simulation code. NASA Report TM-2000-209635, 2000.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2021 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.