Nonlinear acoustic wave propagation in atmosphere
Author:
S. I. Hariharan
Journal:
Quart. Appl. Math. 45 (1987), 735-748
MSC:
Primary 86A35; Secondary 76Q05
DOI:
https://doi.org/10.1090/qam/917023
MathSciNet review:
917023
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Abstract: In this paper we consider a model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
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A. D. Pierce, Propagation of Acoustic Gravity Waves from a Small Source Above the Ground in an Isothermal Atmosphere, J. Acoust. Soc. Am. 35, 1798–1807 (1963)
- Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI https://doi.org/10.1002/cpa.3160230304
S. I. Hariharan and H. C. Lester, A Finite Difference Solution for the Propagation of Sound in Near Sonic Flows, J. Acoust. Soc. Am. 75, 1052–1061 (1984)
S. I. Hariharan and H. C. Lester, Acoustic Shocks in a Variable Area Duct Containing Near Sonic Flows, J. Comp. Phys. 58, 134–145 (1985)
S. I. Hariharan, Numerical Solutions of Acoustic Wave Propagation Problems Using Euler Computations, AIAA-84-2290 (1984)
- K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345–392. MR 62932, DOI https://doi.org/10.1002/cpa.3160070206
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J. D. Cole and C. Greifinger, Acoustic Gravity Waves Produced by Energy Release, Rand Corp. Rept. RM-5738, September 1968
J. D. Cole and C. Greifinger, Acoustic Gravity Waves from an Energy Source at the Ground in an Isothermal Atmosphere, J. of Geophysical Res. 74, 3693–3703 (1969)
A. D. Pierce, Propagation of Acoustic Gravity Waves from a Small Source Above the Ground in an Isothermal Atmosphere, J. Acoust. Soc. Am. 35, 1798–1807 (1963)
H. O. Kreiss, Initial Boundary Value Problems for Hyperbolic Systems, Comm. Pure Appl. Math. 23, 277–298 (1970)
S. I. Hariharan and H. C. Lester, A Finite Difference Solution for the Propagation of Sound in Near Sonic Flows, J. Acoust. Soc. Am. 75, 1052–1061 (1984)
S. I. Hariharan and H. C. Lester, Acoustic Shocks in a Variable Area Duct Containing Near Sonic Flows, J. Comp. Phys. 58, 134–145 (1985)
S. I. Hariharan, Numerical Solutions of Acoustic Wave Propagation Problems Using Euler Computations, AIAA-84-2290 (1984)
K. O. Friedrichs, Symmetric Hyperbolic Linear Differential Equations, Comm. Pure Appl. Math. 7, 345–392 (1954)
H. O. Kreiss, Numerical Methods for Hyperbolic Partial Differential Equations, in Numerical Methods for PDE’s, Academic Press, pp. 213–254, 1979
S. I. Hariharan, Absorbing Boundary Conditions for Exterior Problems, NASA CR-177944 (1985)
B. Engquist and A. Majda, Absorbing Boundary Conditions for the Numerical Simulation of Waves, Math. Comp. 31, 629–651 (1979)
J. D. Cole and C. Greifinger, Acoustic Gravity Waves Produced by Energy Release, Rand Corp. Rept. RM-5738, September 1968
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Article copyright:
© Copyright 1987
American Mathematical Society
