A Characteristic-Based Volume Penalization Method for Arbitrary Mach Flows Around Solid Obstacles

  • Eric Brown-DymkoskiEmail author
  • Nurlybek Kasimov
  • Oleg V. Vasilyev
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 20)


Volume penalization is a subclass of immersed boundary methods for modeling complex geometry flows, which introduces the effects of obstacles by modifying the governing equations.


Supersonic Flow Strouhal Number Oblique Shock General Boundary Condition Inviscid Flow 
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This work was supported by ONR MURI on Soil Blast Modeling and utilized the Janus supercomputer. Janus is supported by the National Science Foundation (award number CNS-0821794) and the University of Colorado Boulder. The Janus supercomputer is a joint effort of the University of Colorado Boulder, the University of Colorado Denver and the National Center for Atmospheric Research.


  1. 1.
    Angot, P., Bruneau, C.-H., Fabrie, P.: A penalization method to take into account obstacles in viscous flows. Numer. Math. 81, 497–520 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ben-Dor, G.: Shock Wave Reflection Phenomena. Springer, New York (2007)Google Scholar
  3. 3.
    Brentner, K.S., Cox, J.S., Rumsey, C.L., Younis, B.A.: Computation of sound generated by flow over a circular cylinder: an acoustic analogy approach. In: Tam, C.K.W., Hardin, J.C. (eds.) Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, pp. 289–295. NASA (1997)Google Scholar
  4. 4.
    Feireisl, E., Neustupa, J., Stebel, S.: Convergence of a Brinkman-type penalization for compressible fluid flows. J. Diff. Equ. 250, 596–606 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Kevlahan, N.K.-R., Ghidaglia, J.-M.: Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman Penalization. Eur. J. Mech. B Fluids 20, 333–350 (2001)CrossRefzbMATHGoogle Scholar
  6. 6.
    Liepmann, H.W., Roshko, A.: Elemenst of Gasdynamics. Dove Publications New York (2001)Google Scholar
  7. 7.
    Liu, Q., Vasilyev, O.V.: Brinkman Penalization method for compressible flows in complex geometries. J. Comput. Phys. 227, 946–966 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Toro, E.: Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer, New York (2009)Google Scholar
  9. 9.
    Vasilyev, O.V., Kevlahan, N.K.-R.: Hybrid wavelet collocation-Brinkman Penalization method for complex geometry flows. Int. J. Numer. Meth. Fluids 40, 531–538 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Wang, A.-B., Trávníček, Z., Chia, K.-C.: On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder. Phys. Fluids 12, 1401–1410 (2000)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Eric Brown-Dymkoski
    • 1
    Email author
  • Nurlybek Kasimov
    • 1
  • Oleg V. Vasilyev
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of Colorado BoulderBoulderUSA

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