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Computational Mathematics and Modeling

, Volume 18, Issue 3, pp 282–309 | Cite as

Artificial boundary conditions for two-dimensional equations of fluid dynamics. 1. Convective wave equation

  • L. V. Dorodnitsyn
Article
  • 46 Downloads

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.

Keywords

Wave Equation Mach Number Plane Wave Incidence Angle Absorb Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. V. Dorodnitsyn, “Acoustic properties of continuous and discrete fluid-dynamic models,” Prikladnaya Matematika i Informatika, No. 6, 39–62 (2000).Google Scholar
  2. 2.
    L. V. Dorodnitsyn, “Nonreflecting boundary conditions for fluid-dynamic systems,” Zh. Vychisl. Matem. i Mat. Fiziki, 42, No. 4, 522–549 (2002).zbMATHMathSciNetGoogle Scholar
  3. 3.
    L. V. Dorodnitsyn, “Artificial boundary conditions for simulation of subsonic gas flows,” Zh. Vychisl. Matem. i Mat. Fiziki, 45, No. 7, 1251–1278 (2005).zbMATHMathSciNetGoogle Scholar
  4. 4.
    V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1985).Google Scholar
  5. 5.
    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).Google Scholar
  6. 6.
    M. B. Giles, “Nonreflecting boundary conditions for Euler equation calculations,” AIAA J., 28, No. 12, 2050–2058 (1990).CrossRefGoogle Scholar
  7. 7.
    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).zbMATHCrossRefGoogle Scholar
  8. 8.
    L. V. Dorodnitsyn, Nonreflecting Boundary Conditions: From a Conception to Algorithms [in Russian], Preprint, MAKS Press, Moscow (2002).Google Scholar
  9. 9.
    D. I. Blokhintsev, Acoustics of a Nonhomogeneous Moving Medium [in Russian], Nauka, Moscow (1981).Google Scholar
  10. 10.
    B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves, ” Math. Comp., 31, No. 139, 629–651 (1977).zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    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).CrossRefMathSciNetGoogle Scholar
  12. 12.
    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.Google Scholar
  13. 13.
    P. Luchini and R. Tognaccini, “Direction-adaptive nonreflecting boundary conditions,” J. Comp. Phys., 128, No. 1, 121–133 (1996).zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    R. L. Higdon, “Initial boundary-value problems for linear hyperbolic systems,” SIAM Rev., 28, No. 2, 177–217 (1986).zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Izd. MGU, Moscow (1999).Google Scholar
  16. 16.
    A. Bayliss and E. Turkel, “Radiation boundary conditions for wave-like equations,” Comm. Pure Appl. Math., 33, No. 6, 707–725 (1980).zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    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).CrossRefMathSciNetGoogle Scholar

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© Springer Science+Business Media, Inc. 2007

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  • L. V. Dorodnitsyn

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