Numerical Ocean Acoustic Propagation in Three Dimensions

The following sections are included:

• Preface

• Contents

Due to the weak three-dimensional effects, most existing ocean acoustic propagation models are aimed at providing solutions to problems that are two-dimensional, i.e. range and depth. Thus, even though the ocean is three-dimensional, the development of three-dimensional models to solve realistic three-dimensional problems has received little attention. Moreover, there is inadequate evidence to indicate the significance of three-dimensional effects…

Successful mathematical modeling leads to the development of a representative mathematical equation that contains as much of the desirable physics as possible. With this in mind, we have focused our development efforts on a three-dimensional, outgoing wave equation. The inclusion of all the desirable physical processes into the mathematical model is conceivable but this approach presents difficulties in finding an efficient solution. In contrast, our basic approach is to develop an accurate mathematical model that is not difficult to solve, even though the representative equation does not contain all the physics we would prefer. The expectation is to develop the mathematical model in such a manner that additional physical mechanisms can be incorporated in subsequent extensions by means of the boundary conditions or the ocean volume…

The following sections are included:

• Siegmann–Kriegsmann–Lee Model

• A Preconditioning Solution

• References

The following sections are included:

• Lee–Saad–Schultz (LSS) Model
  • The LSS Mathematical Model
    • Stability
    • Accuracy

• A Finite Difference Solution

• Model Appraisal

• Computer Code — FOR3D
  • Computer Algorithm: Two-Step Procedure
  • Computation for Step 1
  • Computations for Step 2
  • Computer Model
    • Model capabilities
    • Model structure
    • Geometry of propagation
    • Data structure of the acoustic field
    • Main program FOR3D
    • Subroutines

• References

The following sections are included:

• Density Variation Capability
  • Mathematical Formulation
  • A Numerical Solution
  • Theoretical Justification
    • Interface conditions
    • The numerical treatment of discontinuities
    • Theoretical justification of the numerical treatment
    • Enhanced computer code FOR3D with density variations

• Enhancement of Computation Speed
  • Differential and Difference Operators
  • The Douglas Scheme
    • The Douglas operator
    • Stability
    • Matrix structure
  • A Tridiagonal Solver
  • The Douglas Scheme with Density Variations
    • The Douglas operator with density variations
    • Stability
    • Matrix structure

• References

The following sections are included:

• Exact Solutions

• Test Examples

• Numerical Computations

• References

The following sections are included:

• Concepts of 3D, N × 2D, and 2D
  • Mathematical Classification
  • Computational Classification
  • Physical Classification

• Numerical Examples
  • An Ocean Environment without θ Coupling
  • An Ocean Environment with θ Coupling

• References

This chapter presents a complete listing of the latest version of the computer code, FOR3D, written in FORTRAN language for a CRAY computer. Some program structures of the earlier versions of FOR3D were discussed in Chap. 4. To make the user's life as easy as possible, the FOR3D code was designed to be easy to use and to have as many complete, desirable capabilities as possible. Usage is straightforward and the input runstream format may be found in the program listing. Users should bear in mind that one should take advantage of the code design and ask for the θ-coupling; blind use of the code may neglect some important three-dimensional effects that should not be ignored. Generally, for large-scale propagation problems, supercomputers are required to obtain solutions. These supercomputers may still be time-consuming. Therefore, a constant search for computing speed continues. Users are welcome and encouraged to contribute suggestions…