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Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation
Final rept. 15 May 2005-30 Nov 2008
TENNESSEE UNIV SPACE INST TULLAHOMA
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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 dispersiondiffusion. 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.
APPROVED FOR PUBLIC RELEASE