Water and Wave Applications
Like wind product protoyping and development, water and wave flows are equally time consuming and costly in testing with physical models. Following the successful development and implementation of computer simulation with Vorticity Confinement (VC), mainly used where wind is the flow to be analyzed, Dr. John Steinhoff undertook solving the water and wave prototyping equation. The wave model, Wave Confinement, was developed with the same prinicples in mind as VC, which is to give the scientists a computer model by which thousands of prototypes can be tested in a fraction of the time it takes with either physical testing or conventional computational methods or older computer models.WC includes realistic effects such as varying index of refraction, scattering from complex objects and interference. Unlike other conventional Eulerian schemes, WC does not suffer from numerical dissipation, thereby conserving properties such as total amplitude and other important properties of waves. It generates wave equation solutions as thin solitary waves that can persist on the grid indefinitely.
The property of waves to reflect from boundaries is also captured accurately using WC. That accuracy comes from avoiding use of adaptive boundary grids. In a model using adaptive boundary grids the reflection of waves is responsible for echoes, interference, etc. The energy and momentum of the waves is reflected back with or without 180 degrees phase change depending on the properties of the boundary. The form of a reflected wave front is determined by that of the incident wave front and the surface. Also, boundaries may be complex with many irregularities. Since the innovative WC model does not have this diffusion problem, complex configurations can be accurately captured using very efficient, lower order discretizations with no loss of accuracy. A very effective method for treating reflections can then be implemented that does not require complex surface fitted grids, but allows the surface to be simply ‘immersed’ in a uniform Cartesian grid.
The amount of wave bending due to varying index of refraction depends on the variation in temperature, salinity, and pressure of the medium. WC considers those elements and captures wave fronts in all realistic conditions. The centroid surfaces that propagate accurately on the grid can also be used in newly developed approximations to capture interference. Many conventional schemes that solve frequency which are dependent on the Helmholtz equation, suffer dissipation when computing a rapidly varying field. Also, the time dependent wave equation can be solved using WC as the confinement prevents the unwanted dissipation/reflection/dispersion effects produced by discretization. The effects of complex boundaries are also efficiently captured without having to use fitted or adaptive grids. Refraction of radio waves in evaporated ducts (associated with a sharp drop in moisture immediately above water bodies.) and ionospheric ducts (formed due to variation in electron density) is important in radio wave propagation and is incorporated in the WC model.
