Adaptive solution techniques for simulating underwater explosions and implosions

Adaptive solution techniques are presented for simulating underwater explosions and implosions. The liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space. The solution in water is integrated in time using a semi-implicit time discretization of the adiabatic Euler equations. Results are presented either using a non-conservative semi-implicit algorithm or a conservative semi-implicit algorithm. A semi-implicit algorithm allows one to compute with relatively large time steps compared to an explicit method. The interface solver is based on the coupled level set and volume-of-fluid method (CLSVOF) M. Sussman, A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, J. Comput. Phys. 187 (2003) 110-136; M. Sussman, E.G. Puckett, A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comput. Phys. 162 (2000) 301-337]. Several underwater explosion and implosion test cases are presented to show the performances of our proposed techniques.

[1]  Kenji Takizawa,et al.  The next generation CIP as a conservative semi-Lagrangian solver for solid, liquid and gas , 2002 .

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

[3]  R. Fedkiw,et al.  A numerical method for two-phase flow consisting of separate compressible and incompressible regions , 2000 .

[4]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[5]  P. Wesseling,et al.  A conservative pressure-correction method for flow at all speeds , 2003 .

[6]  John B. Bell,et al.  An Adaptive Mesh Projection Method for Viscous Incompressible Flow , 1997, SIAM J. Sci. Comput..

[7]  Jacob K. White,et al.  A Level Set-Boundary Element Method for the Simulation of Underwater Bubble Dynamics , 2008, SIAM J. Sci. Comput..

[8]  P. Colella,et al.  A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations , 1998 .

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

[10]  Takashi Yabe,et al.  Unified Numerical Procedure for Compressible and Incompressible Fluid , 1991 .

[11]  John B. Bell,et al.  Parallelization of structured, hierarchical adaptive mesh refinement algorithms , 2000 .

[12]  T. Yabe,et al.  The constrained interpolation profile method for multiphase analysis , 2001 .

[13]  Feng Xiao,et al.  Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows , 2006, J. Comput. Phys..

[14]  Andrew B Wardlaw,et al.  Underwater Explosion Test Cases , 1998 .

[15]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[16]  Theo G. Theofanous,et al.  Direct Numerical Simulation of Disperse Multiphase High-Speed Flows , 2004 .

[17]  M. Minion.  A Projection Method for Locally Refined Grids , 1996 .

[18]  John B. Bell,et al.  An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion , 1998 .

[19]  P. Colella,et al.  A Projection Method for Low Speed Flows , 1999 .

[20]  Stanley Osher,et al.  A second order primitive preconditioner for solving all speed multi-phase flows , 2005 .

[21]  Mark Sussman,et al.  A sharp interface method for incompressible two-phase flows , 2007, J. Comput. Phys..

[22]  Cornelis Vuik,et al.  A conservative pressure‐correction method for the Euler and ideal MHD equations at all speeds , 2002 .

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

[24]  P. Wesseling,et al.  Uniformly Effective Numerical Methods for Hyperbolic Systems , 2001, Computing.

[25]  Isidore Rigoutsos,et al.  An algorithm for point clustering and grid generation , 1991, IEEE Trans. Syst. Man Cybern..

[26]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[27]  Phillip Colella,et al.  An Adaptive Semi-Implicit Scheme for Simulations of Unsteady Viscous Compressible Flows , 1995 .

[28]  Marsha Berger,et al.  Three-Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws , 1994, SIAM J. Sci. Comput..

[29]  D. Stevens,et al.  A Forward-in-Time Advection Scheme and Adaptive Multilevel Flow Solver for Nearly Incompressible Atmospheric Flow , 1996 .

[30]  Feng Xiao,et al.  Unified formulation for compressible and incompressible flows by using multi-integrated moments I: one-dimensional inviscid compressible flow , 2004 .

[31]  T. Clark,et al.  Severe Downslope Windstorm Calculations in Two and Three Spatial Dimensions Using Anelastic Interactive Grid Nesting: A Possible Mechanism for Gustiness , 1984 .

[32]  W. Skamarock,et al.  Adaptive Grid Refinement for Two-Dimensional and Three-Dimensional Nonhydrostatic Atmospheric Flow , 1993 .

[33]  Takashi Yabe,et al.  The unified simulation for incompressible and compressible flow by the predictor-corrector scheme based on the CIP method , 1999 .