The Ghost Fluid Method for Numerical Treatment of Discontinuities and Interfaces

The Ghost Fluid Method (GFM) has recently been developed to handle interfaces in a robust and efficient fashion leading to a general class of “boundary condition capturing” techniques based on the identification of “continuous” and “discontinuous” variables and the subsequent treatment of these variables to allow seamless finite differencing across the interface.

[1]  H. Markstein.  Nonsteady flame propagation , 1964 .

[2]  R. Fedkiw,et al.  A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains , 2000 .

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

[4]  W. Davis.  Equation of state for detonation products , 1998 .

[5]  Ralph Menikoff,et al.  Errors When Shock Waves Interact Due to Numerical Shock Width , 1994, SIAM J. Sci. Comput..

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

[7]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[8]  A. Marquina,et al.  Capturing Shock Reeections: an Improved Ux Formula , 1996 .

[9]  James Glimm,et al.  Subgrid resolution of fluid discontinuities, II , 1980 .

[10]  Xiaolin Li,et al.  Simple front tracking , 1999 .

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

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

[13]  Antonio Marquina,et al.  Capturing Shock Reflections , 1996 .

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

[15]  Ronald Fedkiw,et al.  An Isobaric Fix for the Overheating Problem in Multimaterial Compressible Flows , 1999 .

[16]  S. Osher,et al.  Computing interface motion in compressible gas dynamics , 1992 .

[17]  W. F. Noh.  Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux , 1985 .

[18]  P. Lax,et al.  Systems of conservation laws , 1960 .

[19]  E. Puckett,et al.  A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows , 1997 .

[20]  Ronald Fedkiw,et al.  Regular Article: The Ghost Fluid Method for Deflagration and Detonation Discontinuities , 1999 .

[21]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[22]  John B. Bell,et al.  Cartesian grid method for unsteady compressible flow in irregular regions , 1995 .

[23]  Smadar Karni,et al.  Hybrid Multifluid Algorithms , 1996, SIAM J. Sci. Comput..