Abstract
The specification of conditions on artificial boundaries of the computational domain in the simulation of subsonic viscous gas flows is considered. The steps in the construction and implementation of nonreflecting boundary conditions on the path from one-dimensional linearized Euler equations to real-life problems are described. The technique is intended for flow simulation at low Mach numbers. Numerical results for the essentially subsonic flow over a flat plate are presented
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References
M. A. Il’gamov and A. N. Gil’manov, Nonreflecting Conditions on Boundaries of Computational Domains (Fizmatlit, Moscow, 2003) [in Russian].
L. V. Dorodnitsyn, “Transparent Boundary Conditions for Systems of Equations of Gas Dynamics,” Zh. Vychisl. Mat. Mat. Fiz. 42, 522–549 (2002) [Comput. Math. Math. Phys. 42, 499–525 (2002)].
B. N. Chetverushkin, Kinetic Schemes and Quasi-gasdynamic System of Equations (Maks Press, Moscow, 2004) [in Russian].
V. S. Ryaben’kii, “Accurate Transfer of Boundary Conditions,” Vychisl. Mekh. Deform. Tverdogo Tela, No. 1, 129–145 (1990).
D. Givoli, “Nonreflecting Boundary Conditions,” J. Comput. Phys. 94(1), 1–29 (1991).
S. V. Tsynkov, “Numerical Solution of Problems on Unbounded Domains: A Review,” Appl. Numer. Math. 27, 465–532 (1998).
V. S. Ryaben’kii, The Method of Difference Potentials and Its Applications (Fizmatlit, Moscow, 2010) [in Russian].
B. Engquist and A. Majda, “Absorbing Boundary Conditions for the Numerical Simulation of Waves,” Math. Comput. 31(139), 629–651 (1977).
L. N. Trefethen and L. Halpern, “Well-Posedness of One-Way Wave Equations and Absorbing Boundary Conditions,” Math. Comput. 47(176), 421–435 (1986).
M. B. Giles, “Nonreflecting Boundary Conditions for Euler Equation Calculations,” AIAA J. 28, 2050–2058 (1990).
L. V. Dorodnitsyn, “Artificial Boundary Conditions for Numerical Simulation of Subsonic Gas Flows,” Zh. Vychisl. Mat. Mat. Fiz. 45, 1251–1278 (2005) [Comput. Math. Math. Phys. 45, 1209–1234 (2005)].
F. Q. Hu, “On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer,” J. Comput. Phys. 129(1), 201–219 (1996).
L. V. Dorodnitsyn, “Artificial Boundary Conditions for Two-Dimensional Gas Dynamics Equations: 1. Wave Equation with Convection,” in Applied Mathematics and Informatics (Maks Press, Moscow, 2006), No. 24, pp. 76–110 [in Russian].
R. L. Higdon, “Initial-Boundary Value Problems for Linear Hyperbolic Systems,” SIAM Rev. 28(2), 177–217 (1986).
A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).
A. B. Al’shin, E. A. Al’shina, and N. N. Kalitkin, “Numerical Solution of Hyperbolic Problems in Unbounded Domains,” Mat. Model. 16(4), 114–126 (2004).
B. Gustafsson, High Order Difference Methods for Time Dependent PDE (Springer-Verlag, Berlin, 2008).
G. W. Hedstrom, “Nonreflecting Boundary Conditions for Nonlinear Hyperbolic Systems,” J. Comput. Phys. 30(2), 222–237 (1979).
B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Applications to Gas Dynamics (Nauka, Moscow, 1978) [in Russian].
A. T. Fedorchenko, “Numerical Simulation of Unsteady Three-Dimensional Viscous Gas Flows in Nozzles,” Zh. Vychisl. Mat. Mat. Fiz. 22, 178–196 (1982).
A. T. Fedorchenko, “Nonlinear Models of Sound-Absorbing Boundary Cross Sections of the Computational Domain of a Channel,” Akust. Zh. 30, 827–833 (1984).
D. H. Rudy and J. C. Strikwerda, “A Nonreflecting Outflow Boundary Condition for Subsonic Navier-Stokes Calculations,” J. Comput. Phys. 36(1), 55–70 (1980).
T. J. Poinsot and S. K. Lele, “Boundary Conditions for Direct Simulations of Compressible Viscous Flows,” J. Comput. Phys. 101(1), 104–129 (1992).
A. A. Dorodnicyn, “Boundary Layer in Compressible Gas,” Prikl. Mat. Mekh. 6, 449–486 (1942).
L. V. Dorodnitsyn and B. N. Chetverushkin, “Implicit Scheme for Subsonic Gas Flow Simulation,” Mat. Model. 9(5), 108–118 (1997).
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Dedicated to Academician A.A. Dorodnicyn on the Occasion of the Centenary of His Birth
Original Russian Text © L.V. Dorodnicyn, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 1, pp. 152–162.
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Dorodnicyn, L.V. Nonreflecting boundary conditions and numerical simulation of external flows. Comput. Math. and Math. Phys. 51, 143–159 (2011). https://doi.org/10.1134/S0965542511010076
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DOI: https://doi.org/10.1134/S0965542511010076