• Title/Summary/Keyword: Roe's theorem

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SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS

  • Mejjaoli, Hatem
    • Korean Journal of Mathematics
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    • v.24 no.4
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    • pp.693-722
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    • 2016
  • In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

Internal Wave Computations based on a Discontinuity in Dynamic Pressure (동압 계수의 불연속성을 이용한 내면파의 수치해석)

  • 신상묵;김동훈
    • Journal of the Society of Naval Architects of Korea
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    • v.41 no.4
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    • pp.17-29
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    • 2004
  • Internal waves are computed using a ghost fluid method on an unstructured grid. Discontinuities in density and dynamic pressure are captured in one cell without smearing or oscillations along a multimaterial interface. A time-accurate incompressible Navier-Stokes/Euler solver is developed based on a three-point backward difference formula for the physical time marching. Artificial compressibility is introduced with respect to pseudotime and an implicit method is used for the pseudotime iteration. To track evolution of an interface, a level set function is coupled with the governing equations. Roe's flux difference splitting method is used to calculate numerical fluxes of the coupled equations. To get higher order accuracy, dependent variables are reconstructed based on gradients which are calculated using Gauss theorem. For each edge crossing an interface, dynamic pressure is assigned for a ghost node to enforce the continuity of total pressure along the interface. Solitary internal waves are computed and the results are compared with other computational and experimental results.