Abstract
A mathematical model consisting of quasi-hydrodynamic equations and Dong’s outflow boundary conditions is proposed for solving fluid dynamics problems in a truncated computational domain. A solution algorithm based on finite-element and control-volume methods is developed. The Kovasznay flow and the flow over a backward-facing step in truncated computational domains are numerically simulated. A comparative analysis of the numerical results shows that the proposed mathematical model adequately describes the hydrodynamic flows in a truncated domain.
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REFERENCES
I. Orlanski, “A simple boundary condition for unbounded hyperbolic flows,” J. Comput. Phys. 21, 251–269 (1976).
G. W. Hedstrom, “Nonreflecting boundary conditions for nonlinear hyperbolic systems,” J. Comput. Phys. 30, 222–237 (1979).
D. H. Rudy and J. C. Strikwerda, “A nonreflecting outflow boundary condition for subsonic Navier–Stokes calculations,” J. Comput. Phys. 36, 55–70 (1980).
T. C. Papanastasiou, N. Malamataris, and K. Ellwood, “A new outflow boundary condition,” Int. J. Numer. Methods Fluids 14, 587–608 (1992).
M. Braack and P. B. Mucha, “Directional do-nothing condition for the Navier–Stokes equations,” J. Comput. Math. 32, 507–521 (2014).
S. Dong, G. E. Karniadakis, and C. Chryssostomidis, “A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains,” J. Comput. Phys. 261, 83–105 (2014). https://doi.org/10.1016/j.jcp.2013.12.042
J.-E. W. Lombard, D. Moxey, J. F. A. Hoessler, S. Dhandapani, M. J. T. Taylor, and S. J. Sherwin, “Implicit large-eddy simulation of a wingtip vortex,” AIAA J. 54 (2), 1–13 (2015).
C. D. Cantwella, D. Moxeya, A. Comerforda, A. Bolisa, G. Roccoa, G. Mengaldoa, D. de Graziaa, S. Yakovlevb, J.-E. Lombarda, D. Ekelschota, B. Jordia, H. Xua, Y. Mohamieda, C. Eskilssonc, B. Nelsonb, P. Vosa, C. Biottoa, R. M. Kirbyb, and S. J. Sherwin, Nektar++: An Open-Source Spectral/Element Framework (CPC, 2015).
Ph. Miron and J. Vétel, “Towards the detection of moving separation in unsteady flows,” J. Fluid Mech. 779, 819–841 (2015).
P. Fan, “The standard upwind compact difference schemes for incompressible flow simulations,” J. Comput. Phys. 322, 74–112 (2016).
A. Q. Garcia, A. A. Gomes, and M. B. Hecke, “On the performance of the DG method with a directional do-nothing boundary condition,” J. Braz. Soc. Mech. Sci. Eng. 39 (10), 3919–3929 (2017).
Y. T. Delorme, K. Puri, J. Nordstrom, V. Linders, S. Dong, and S. H. Frankel, “A simple and efficient incompressible Navier–Stokes solver for unsteady complex geometry flows on truncated domains,” Comput. Fluids 150, 84–94 (2017).
T. G. Elizarova, Quasi-Gas Dynamic Equations (Nauchnyi Mir, Moscow, 2007; Springer, Berlin, 2009).
T. G. Elizarova, “Time averaging as an approximate technique for constructing quasi-gasdynamic and quasi-hydrodynamic equations,” Comput. Math. Math. Phys. 51 (11), 1973–1982 (2011).
K. S. Snigur, Candidate’s Dissertation in Mathematics and Physics (Computing Center, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, 2016).
L. I. G. Kovasznay, “Laminar flow behind a two-dimensional grid,” Math. Proc. Cambridge 44 (1), 58–62 (1948).
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ACKNOWLEDGMENTS
This research was supported through computational resources provided by the Shared Facility Center “Data Center of FEB RAS” [17].
This work was funded by the Russian Foundation for Basic Research, project nos. 18-05-00530, 18-35-00139.
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Translated by I. Ruzanova
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Potapov, I.I., Snigur, K.S. Solution of Fluid Dynamics Problems in Truncated Computational Domains. Comput. Math. and Math. Phys. 59, 484–492 (2019). https://doi.org/10.1134/S0965542519030138
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DOI: https://doi.org/10.1134/S0965542519030138