Accession Number : ADA506308


Title :   Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation


Descriptive Note : Final rept. 15 May 2005-30 Nov 2008


Corporate Author : TENNESSEE UNIV SPACE INST TULLAHOMA


Personal Author(s) : Steinhoff, John


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a506308.pdf


Report Date : Jul 2009


Pagination or Media Count : 43


Abstract : A new numerical method, Wave Confinement (WC), is developed to efficiently solve the linear wave equation. This is similar to the originally developed Vorticity Confinement method for fluid mechanics problems. It involves modification of the discrete wave equation by adding an extra nonlinear term that can accurately propagate the pulses for long distances without numerical dispersion/diffusion. These pulses are propagated as stable codimension-one surfaces and do not suffer phase shift or amplitude exchange in spite of nonlinearity. The pulses remain thin unlike conventional higher order numerical schemes, which only converge as N (number of grid cells across the pulse) becomes large. The additional term does not interfere with conservation of the important integral quantities such as total amplitude, centroid. Also, properties like varying index of refraction, diffraction, multiple reflections are included and tested.


Descriptors :   *ATMOSPHERIC REFRACTION , *WAVE EQUATIONS , REFRACTIVE INDEX , REFLECTION , LONG RANGE(TIME) , NONLINEAR SYSTEMS , LINEAR DIFFERENTIAL EQUATIONS , AMPLITUDE , FLUID MECHANICS , PHASE SHIFT , NUMERICAL ANALYSIS , DISPERSING , DIFFUSION


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE