Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics

  • Authors:

  • Hailiang Liu;Zhongming Wang

  • Affiliations:

  • Mathematics Department, Iowa State University, Ames, USA 50011;Mathematics Department, Iowa State University, Ames, USA 50011

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2008

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Abstract

The weakly coupled WKB system captures high frequency wave dynamics in many applications. For such a system a level set method framework has been recently developed to compute multi-valued solutions to the Hamilton-Jacobi equation and evaluate position density accordingly. In this paper we propose two approaches for computing multi-valued quantities related to density, momentum as well as energy. Within this level set framework we show that physical observables evaluated in Jin et al. (J. Comput. Phys. 210(2):497---518, [2005]; J. Comput. Phys. 205(1):222---241, [2005]) are simply the superposition of their multi-valued correspondents. A series of numerical tests is performed to compute multi-valued quantities and validate the established superposition properties.