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Universal and Simultaneous Solution of Solid, Liquid and Gas in Cartesian-Grid-Based CIP Method

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Mathematical Modeling and Numerical Simulation in Continuum Mechanics

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 19))

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Abstract

We present a review of the CIP method that is known as a general numerical solver for solid, liquid and gas. This method is a kind of semi-Lagrangean scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it suits for multi-phase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangean scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and subcell resolution including front capturing algorithm with functional transformation. Some practical applications are also reviewed such as milk crown or coronet.

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Author information

Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, 152-8552, Japan

    Takashi Yabe

Authors
  1. Takashi Yabe
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Editor information

Editors and Affiliations

  1. Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, WRW 215, C0600, Austin, Texas, 78712-1085, USA

    Ivo Babuška

  2. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Boîte courrier 187, 75252, Paris cedex 05, France

    Philippe G. Ciarlet

  3. Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, 753-8512, Yamaguchi, Japan

    Tetsuhiko Miyoshi

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© 2002 Springer-Verlag Berlin Heidelberg

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Yabe, T. (2002). Universal and Simultaneous Solution of Solid, Liquid and Gas in Cartesian-Grid-Based CIP Method. In: Babuška, I., Ciarlet, P.G., Miyoshi, T. (eds) Mathematical Modeling and Numerical Simulation in Continuum Mechanics. Lecture Notes in Computational Science and Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56288-4_5

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  • DOI: https://doi.org/10.1007/978-3-642-56288-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42399-7

  • Online ISBN: 978-3-642-56288-4

  • eBook Packages: Springer Book Archive

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