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The Numerical Investigation of the Two-dimensional Shock Wave Reflection

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Abstract

In this contribution we present recent stability results concerning the numerical approximation of initial-boundary value problems for the equations of fluid motion. Our special interest is aimed at the process of the reflection of fluid motion from an impermeable boundary — an oblique wall.

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References

  1. B. Gustafsson, H.-O. Kreiss, A. Sundström, Stability Theory of Difference Approximations for Mixed Initial-Boundary Value Problems. II, Math. Comp., Vol. 26, No. 119, 649–686 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. K. Kantiem, Numerical Investigation of the two-dimensional Shock Wave Reflection, Arch. Mech. 46, 5, 639–651 (1994)

    MathSciNet  MATH  Google Scholar 

  3. K. Kantiem, On numerical Stability of Boundary Conditions for the Equations of Fluid Mechanics, Ph.D. Thesis, Warsaw University 1994, Warsaw (Poland )

    Google Scholar 

  4. K. Kantiem, W. Zaj’Czkowski, The Existence and Uniqueness of Solutions of Equations for Ideal Compressible Polytropic Fluids, to appear

    Google Scholar 

  5. R. W. Maccormack, Numerical Solution of the Interaction of a Shock Wave with a Laminar Boundary Layer, Proceedings of the 2nd International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics 8, 151–163 (1970)

    Article  Google Scholar 

  6. D. Michelson, Stability Theory of Difference Approximations for Multidimensional Initial-Boundary Value Problems, Math. Comp., Vol. 40, No. 161, 1–45 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. T. J. Poinsot, S. K. Lele, Boundary Conditions for Direct Simulations of Compressible Viscous Flows, J. Comp. Phys. 101, 104–129 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Rauch, Symmetric Positive Systems with Boundary Characteristic of Constant Multiplicity, Trans. AMS 291, No. 1, 167–187 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. P. Secchi, The Initial Boundary Value Problem for Linear Hyperbolic Systems with Characteristic Boundary of Constant Multiplicity, Pisa Univ., Dept. of Math., preprint 2. 153 (768), 1993

    Google Scholar 

  10. A. Tani, On the First Initial-Boundary Value Problem of Compressible Viscous Fluid Motion, Publ. Res. Inst. Math. Sci. 13, 193–253 (1977)

    Article  MATH  Google Scholar 

  11. A. Valli, An Existence Theorem for Compressible Viscous Fluids, Ann. Mat. Pura Appl. (IV) 130, 197–213 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  12. Z. A. Walenta, private communication

    Google Scholar 

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© 1996 John Wiley & Sons Ltd and B. G. Teubner

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Kantiem, K., Palczewski, A. (1996). The Numerical Investigation of the Two-dimensional Shock Wave Reflection. In: Neunzert, H. (eds) Progress in Industrial Mathematics at ECMI 94. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-82967-2_8

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  • DOI: https://doi.org/10.1007/978-3-322-82967-2_8

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-82968-9

  • Online ISBN: 978-3-322-82967-2

  • eBook Packages: Springer Book Archive

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