By D. Lee, S. T. McDaniel
A concise consultant to the speculation and alertness of numerical tools for predicting ocean acoustic propagation, additionally delivering an advent to numerical tools, with an summary of these tools almost immediately in use. An in-depth improvement of the implicit-finite-difference procedure is gifted including bench-mark attempt examples incorporated to illustrate its software to reasonable ocean environments. different functions comprise atmospheric acoustics, plasma physics, quantum mechanics, optics and seismology
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Additional info for Ocean Acoustic Propagation by Finite Difference Methods
2. S. T. McDaniel, Applications of energy methods to finite-difference solutions of the parabolic wave equation. In Computational Ocean Acoustics (Eds M. H. Schultz and D. Lee). Pergamon Press, Oxford (1985). 3. A. D. Pierce, The natural reference wavenumber for parabolic approximations in ocean acoustics. In Computational Ocean Acoustics (Eds M. H. Schultz and D. Lee). Pergamon Press, Oxford (1985). 35). The above equation, as discussed previously, can be obtained in a number of ways. 33) urr + 2 ik0ur + uzz + kl(n2(r, z) - \)u = 0, on the basis of the assumption, \urr\ <ζ \2ik0ur\.
In doing so, we consider the following. 40), we have t W J t a « . 43), respectively. In addition, we require a finite difference representation for the range derivative of the field away from the interface. We use a second order central difference operator for uzz. In medium 1, (ux)nm+x satisfies the parabolic wave equation, δ(μ £* x +l + ! Y ++ +^(<« -* - ^ . 44) Similarly, in medium 2, (w2)m+i satisfies the PE, ^ N = (flzfi +1 te)t+1 + p ((«2Ä + 2 - 2(t/ 2 t + , + M ) . Ä + J, + («,)-+,1) ii+|(«,-/»,-y,)l ==^ 1 + χ ( « .
2. F. R. DiNapoli and R. L. Deavenport, Numerical models of underwater acoustic propagation. In Topics in Current Physics (Ed. J. A. DeSanto). Springer, Berlin (1979). 340 D. LEE and S. T. MCDANIEL 3. B. Carnahan, H. A. Luther and J. O. Wikes, In Applied Numerical Methods. Wiley, New York (1969). 4. D. Lee, G. Botseas and J. S. Papadakis, Finite-difference solution to the parabolic wave equation. J. acoust. Soc. Am. 70 (8), 795-800 (1981). 5. S. T. McDaniel and D. Lee, A finite-difference treatment of interface conditions for the parabolic wave equation: the horizontal interface.
Ocean Acoustic Propagation by Finite Difference Methods by D. Lee, S. T. McDaniel