, Volume 31, Issue 6, pp 697–707 | Cite as

A level set formulation for the numerical simulation of impact of surge fronts

  • A. Salih
  • S. Ghosh Moulic


In this paper we present a level set-based algorithm for the solution of incompressible two-phase flow problems. The technique is applied to the numerical simulation of impact of two surge fronts resulting from the collapse of liquid columns. The incompressible Navier-Stokes equations are solved using a projection method based on forward Euler time-stepping. The Hamilton-Jacobi type equation for the transport of level set function is carried out by a high resolution fifth-order accurate WENO scheme. For efficient implementation of the WENO scheme we have proposed grid staggering for the level set function. The solution of the pressure Poisson equation is obtained using an efficient preconditioned conjugate gradient method. It is shown that the present formulation works very well for large density and viscosity ratios. For the purpose of validation, we have simulated small-amplitude free sloshing of liquid in a container and the well-known two-dimensional broken-dam problem of Martin and Moyce. Simulations of impact of surge fronts have been carried out and the results are discussed.


Free surface flows level set methods impact of surge fronts 


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  1. Chang Y C, Hou T Y, Merriman B, Osher S 1996 A level set Formulation of eulerian interface capturing methods for incompressible fluid flows.J. Comput. Phys. 124: 449–464MATHCrossRefMathSciNetGoogle Scholar
  2. Floryan J M, Rasmussen H 1989 Numerical methods for viscous flows with moving boundaries.Appl. Mech. Rev. 42: 323–340MathSciNetCrossRefGoogle Scholar
  3. Golub G, Van Loan C 1996Matrix computations 3rd edn (Baltimore: The Johns Hopkins University Press)MATHGoogle Scholar
  4. Jiang G-S, Peng D 2000 Weighted ENO schemes for Hamilton-Jacobi equations.SIAM J. Sci. Comput. 21:2126–2143MATHCrossRefMathSciNetGoogle Scholar
  5. Harlow F H, Welch J E 1965 Numerical study of large-amplitude free-surface motions.Phys. Fluids 8: 2182–2189CrossRefGoogle Scholar
  6. Hirt C W, Nichols B D 1981 Volume of fluid (VOF) methods for dynamics of free boundaries.J. Comput. Phys. 39: 201–225MATHCrossRefGoogle Scholar
  7. Martin J C, Moyce W J 1952 An experimental study of the collapse of liquid columns on a rigid horizontal plane.Philos. Trans. R. Soc. A224: 312–324CrossRefGoogle Scholar
  8. Osher S, Fedkiw R 2001 Level set methods: An overview and some recent results,J. Comput. Phys. 169: 463–502MATHCrossRefMathSciNetGoogle Scholar
  9. Osher S, Sethian J A 1988 Fronts propagating with curvature-dependent speed: Algorithm based on Hamilton-Jacobi formulations.J. Comput. Phys. 79: 12–49MATHCrossRefMathSciNetGoogle Scholar
  10. Peyret R, Taylor T D 1983Computational methods for fluid flow (Springer-Verlag, New York)MATHGoogle Scholar
  11. Salih A 2007Numerical simulation of two-fluid flows with sharp interfaces using level set method PhD thesis, Indian Institute of Technology, KharagpurGoogle Scholar
  12. Scardovelli R, Zaleski S 1999 Direct numerical simulation of free-surface and interfacial flow.Annu. Rev. Fluid Mech. 31: 567–603CrossRefMathSciNetGoogle Scholar
  13. Sethian J A 1999Level set methods and fast marching methods (Cambridge: University Press)MATHGoogle Scholar
  14. Sethian J A, Smereka P 2003 Level set methods for fluid interfaces.Annu. Rev. Fluid Mech. 35: 341–372CrossRefMathSciNetGoogle Scholar
  15. Stoker J J 1992Water waves: The mathematical theory with applications 2nd edn (New York: Wiley Interscience)MATHGoogle Scholar
  16. Sussman M, Smereka P, Osher S 1994 A level set approach for computing solutions to incompressible two-phase flow.J. Comput. Phys. 114: 146–159MATHCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  • A. Salih
    • 1
  • S. Ghosh Moulic
    • 2
  1. 1.Department of Mechanical EngineeringNational Institute of TechnologyTiruchirappalliIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia

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