On the application of the single-phase level set method to naval hydrodynamic flows

Abstract The application of the single-phase level set approach to the numerical simulations of three-dimensional free surface flows around complex geometries, at both non-breaking and breaking regimes is presented. In this approach only the liquid phase is simulated and the level set function is used as tracking device to locate the free surface position. The extrapolation of the solution in the dummy points in the gaseous phase is such that second-order accuracy is maintained also in the points adjacent to the free surface; the time evolution of the level set function and the re-initialization step have been merged so to get a function which is a distance function everywhere, and satisfies, at the same time, the kinematic condition on the free surface. The implementation of this technique into a general purpose Reynolds averaged Navier–Stokes (RANS) equations solver developed at INSEAN [Di Mascio A, Broglia R, Favini B. A Second Order Godunov-type Scheme for Naval Hydrodynamics. Kluwer Academic/Plenum Publishers; 2001, p. 253–61], is described in details; capabilities of the algorithm in dealing with non-breaking and breaking flows in the naval hydrodynamic context will be demonstrated by using a submerged hydrofoil and two different ship hulls in straight course as test cases. Comparisons with both experimental data and numerical surface fitting computations are presented; convergence properties of the algorithm, as well as validation and verification assessment will be also discussed.

[1]  Ronald Fedkiw,et al.  A Boundary Condition Capturing Method for Multiphase Incompressible Flow , 2000, J. Sci. Comput..

[2]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[3]  Frederick Stern,et al.  Statistical Approach for Estimating Intervals of Certification or Biases of Facilities or Measurement Systems Including Uncertainties , 2005 .

[4]  S. Osher,et al.  An improved level set method for incompressible two-phase flows , 1998 .

[5]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[6]  James H. Duncan,et al.  The breaking and non-breaking wave resistance of a two-dimensional hydrofoil , 1983, Journal of Fluid Mechanics.

[7]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[8]  R. Fedkiw,et al.  USING THE PARTICLE LEVEL SET METHOD AND A SECOND ORDER ACCURATE PRESSURE BOUNDARY CONDITION FOR FREE SURFACE FLOWS , 2003 .

[9]  M. Sussman.  A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles , 2003 .

[10]  Lars Larsson,et al.  Level Set Methods for Predicting Viscous Free Surface Flows , 1999 .

[11]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[12]  Frederick Stern,et al.  Unsteady RANS simulation of the ship forward speed diffraction problem , 2006 .

[13]  Riccardo Broglia,et al.  A Level Set Approach For Naval Applications , 2003 .

[14]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[15]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[16]  Joseph Katz,et al.  On the structure of bow waves on a ship model , 1997, Journal of Fluid Mechanics.

[17]  P. Smereka,et al.  A Remark on Computing Distance Functions , 2000 .

[18]  James A. Sethian,et al.  The Fast Construction of Extension Velocities in Level Set Methods , 1999 .

[19]  Woo Il Lee,et al.  A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface‐tracking algorithm and its verification , 2003 .

[20]  Roberto Muscari,et al.  A model for the simulation of steady spilling breaking waves , 2003 .

[21]  Yasuyuki Toda,et al.  MEAN-FLOW MEASUREMENTS IN THE BOUNDARY LAYER AND WAKE AND WAVE FIELD OF A SERIES 60 CB=0.6 SHIP MODEL - PART 1: FROUDE NUMBERS 0.16 AND 0.316 , 1992 .

[22]  Shin Hyung Rhee,et al.  RANS Model for Spilling Breaking Waves , 2002 .

[23]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[24]  Frederick Stern,et al.  Towing Tank Experiments of Resistance, Sinkage and Trim, Boundary Layer, Wake, and Free Surface Flow Around a Naval Combatant Insean 2340 Model , 2001 .

[25]  Frederic Raichlen,et al.  Bow Wave Dynamics , 2002 .

[26]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[27]  Riccardo Broglia,et al.  MULTIGRID ACCELERATION OF SECOND‐ORDER ENO SCHEMES FROM LOW SUBSONIC TO HIGH SUPERSONIC FLOWS , 1996 .

[28]  Hugh W. Coleman,et al.  International Collaboration on Benchmark CFD Validation Data for Surface Combatant DTMB Model 5415 , 2001 .

[29]  Mark Sussman,et al.  The Numerical Simulation of Ship Waves using Cartesian Grid Methods , 2014, 1410.1952.

[30]  Ronald Fedkiw,et al.  Practical animation of liquids , 2001, SIGGRAPH.

[31]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[32]  J. Sethian.  Evolution, implementation, and application of level set and fast marching methods for advancing fronts , 2001 .

[33]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[34]  Mark Sussman,et al.  An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow , 1999, SIAM J. Sci. Comput..

[35]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[36]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[37]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[38]  R. Fedkiw,et al.  A boundary condition capturing method for incompressible flame discontinuities , 2001 .

[39]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[40]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[41]  Frederick Stern,et al.  An unsteady single‐phase level set method for viscous free surface flows , 2007 .

[42]  Riccardo Broglia,et al.  A Second Order Godunov-Type Scheme for Naval Hydrodynamics , 2001 .

[43]  J. Sethian,et al.  LEVEL SET METHODS FOR FLUID INTERFACES , 2003 .

[44]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[45]  P. Roache.  QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS , 1997 .