By D. Lee, S. T. McDaniel
A concise advisor to the idea and alertness of numerical equipment for predicting ocean acoustic propagation, additionally offering an advent to numerical equipment, with an summary of these tools shortly in use. An in-depth improvement of the implicit-finite-difference method is gifted including bench-mark attempt examples integrated to illustrate its software to reasonable ocean environments. different purposes contain atmospheric acoustics, plasma physics, quantum mechanics, optics and seismology
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Extra info for Ocean Acoustic Propagation by Finite Difference Methods
Recalling that the standard PE takes the form, / , i "r = 2 ko(* (r, z) - l)w + — uzz. 2) at r =r0 + Ar assumes that the solution takes the form f'o + Ar Γ w(r,z) = exp / f'0 + ΔΓ A(r,z)dr+i Π B(z)dr \u(r0,z). 5) requires that the commutator [(A + B\ \(A + B) d r l = 0. 6) In general, this commutator will identically vanish only if A(r9 z) is independent of z. This case is of trivial importance for oceanic acoustic propagation. 6) restricts the 361 D. LEE and S. T. 5) to environments in which A is sufficiently slowly varying with depth that the error incurred is negligible.
LEE and S. T. 16) hold for an interface of arbitrary slope. 2. Mathematical formulation of the wave field on the interface To formulate finite difference equations for the wave field on the interface, we will use a mesh having a uniform partition in the z direction with Az = h. The range is partitioned in increments Ar = k, as is shown in Fig. 7. At each mesh point, superscripts are used to indicate the range level; subscripts indicate the depth level. The wave field at the point (nk, mh) is written as unm which also denotes the field on the interface.
Below, we will show how special handling of the bottom boundary condition plus a pressure release surface allow the nonzero bottom component to be incorporated into the A matrix thus making g(k0, r, z, u) totally independent of u. This allows the use of a large step size. 20) h<\. 20). This treatment does not necessarily require using implicit methods. Carrying out the application for low accuracy requirements, the following formula is used, in which the order k is chosen to be 1, and the method is chosen to be explicit.