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

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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2009
Accession Number
ADA506308

Entities

People

  • John Steinhoff

Organizations

  • University of Tennessee Space Institute

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Amplitude
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Diffraction
  • Equations
  • Fluid Dynamics
  • Partial Differential Equations
  • Refraction
  • Refractive Index
  • Scattering
  • Solitons
  • Two Dimensional
  • Wave Equations
  • Wave Phenomena
  • Wave Propagation
  • Waves

Fields of Study

  • Physics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Computational Fluid Dynamics (CFD)