Abstract
The article models external flow problems on artificially bounded regions. In the linear approximation we examine the reflection of acoustic waves in a moving medium, incident at various angles on a fixed boundary. We consider the construction of various boundary conditions and estimate their reflecting properties for plane waves and waves from point sources. The plane wave approximation is justified theoretically. A method is proposed for estimating the integral reflection coefficient for waves with a whole range of incidence angles.
Similar content being viewed by others
References
L. V. Dorodnitsyn, “Acoustic properties of continuous and discrete fluid-dynamic models,” Prikladnaya Matematika i Informatika, No. 6, 39–62 (2000).
L. V. Dorodnitsyn, “Nonreflecting boundary conditions for fluid-dynamic systems,” Zh. Vychisl. Matem. i Mat. Fiziki, 42, No. 4, 522–549 (2002).
L. V. Dorodnitsyn, “Artificial boundary conditions for simulation of subsonic gas flows,” Zh. Vychisl. Matem. i Mat. Fiziki, 45, No. 7, 1251–1278 (2005).
V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1985).
A. T. Fedorchenko, “Reflection of a plane sound wave from a permeable surface in the presence of a normal gas flow,” Akust. Zh., 35, No. 5, 951–953 (1989).
M. B. Giles, “Nonreflecting boundary conditions for Euler equation calculations,” AIAA J., 28, No. 12, 2050–2058 (1990).
F. Q. Hu, “On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer,” J. Comp. Phys., 129, No. 1, 201–219 (1996).
L. V. Dorodnitsyn, Nonreflecting Boundary Conditions: From a Conception to Algorithms [in Russian], Preprint, MAKS Press, Moscow (2002).
D. I. Blokhintsev, Acoustics of a Nonhomogeneous Moving Medium [in Russian], Nauka, Moscow (1981).
B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves, ” Math. Comp., 31, No. 139, 629–651 (1977).
L. N. Trefethen and L. Halpern, “Well-posedness of one-way wave equations and absorbing boundary conditions,” Math. Comp., 47, No. 176, L 421–435 (1986).
M. A. Il’gamov, “On nonreflecting conditions on boundaries of a simulation region,” in: Dynamics of Shells in a Flow [in Russian], Proceedings of a Seminar, No. 18, KFTI KF AN SSSR, Kazan’ (1985), pp. 4–76.
P. Luchini and R. Tognaccini, “Direction-adaptive nonreflecting boundary conditions,” J. Comp. Phys., 128, No. 1, 121–133 (1996).
R. L. Higdon, “Initial boundary-value problems for linear hyperbolic systems,” SIAM Rev., 28, No. 2, 177–217 (1986).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Izd. MGU, Moscow (1999).
A. Bayliss and E. Turkel, “Radiation boundary conditions for wave-like equations,” Comm. Pure Appl. Math., 33, No. 6, 707–725 (1980).
T. Hagstrom, S. I. Hariharan, and D. Thompson, “High-order radiation boundary conditions for the convective wave equation in exterior domains,” SIAM J. Sci. Comp., 25, No. 3, 1088–1101 (2004).
Additional information
__________
Translated from Prikladnaya Matematika i Informatika, No. 24, pp. 76–110, 2006.
Rights and permissions
About this article
Cite this article
Dorodnitsyn, L.V. Artificial boundary conditions for two-dimensional equations of fluid dynamics. 1. Convective wave equation. Comput Math Model 18, 282–309 (2007). https://doi.org/10.1007/s10598-007-0026-8
Issue Date:
DOI: https://doi.org/10.1007/s10598-007-0026-8