A multi-resolution method for two-phase fluids with complex equations of state by binomial solvers in three space dimensions

Abstract In this paper, we propose approximate solvers for two-phase fluids with general equations of state (EOS) in high dimension. The standard finite volume scheme is used for each fluid away from material interface. The two-phase interfaces are captured by the level set method coupled with a multi-resolution algorithm. For the Riemann solver of two-phase fluids with general equations of state, we construct an iterative approximation method by the solver for binomial equations of state. The velocity of the interface and the interface exchange fluxes are obtained precisely. With the help of the adaptive multi-resolution algorithms, we extend the method to three space dimensions conveniently. Numerical examples are carried out to demonstrate the strength and robustness of this method.

[1]  M. Rudman.  INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 24, 671–691 (1997) VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS , 2022 .

[2]  Hiroshi Terashima,et al.  A front-tracking/ghost-fluid method for fluid interfaces in compressible flows , 2009, J. Comput. Phys..

[3]  Boo Cheong Khoo,et al.  The ghost fluid method for compressible gas-water simulation , 2005 .

[4]  Nikolaus A. Adams,et al.  Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure , 2014, J. Comput. Phys..

[5]  Boo Cheong Khoo,et al.  Ghost fluid method for strong shock impacting on material interface , 2003 .

[6]  A. Harten.  Adaptive Multiresolution Schemes for Shock Computations , 1994 .

[7]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

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

[9]  Phillip Colella,et al.  Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems , 2007, J. Comput. Phys..

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

[11]  R. LeVeque,et al.  Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems , 1998 .

[12]  Keh-Ming Shyue,et al.  A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions , 2006, J. Comput. Phys..

[13]  Nikolaus A. Adams,et al.  A conservative interface method for compressible flows , 2006, J. Comput. Phys..

[14]  Xiaolin Li,et al.  A Robust Front Tracking Method: Verification and Application to Simulation of the Primary Breakup of a Liquid Jet , 2011, SIAM J. Sci. Comput..

[15]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

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

[17]  Zhiliang Xu,et al.  Conservative Front Tracking with Improved Accuracy , 2003, SIAM J. Numer. Anal..

[18]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[19]  Diego Rossinelli,et al.  High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions , 2010, J. Comput. Phys..

[20]  Heinz Pitsch,et al.  An accurate conservative level set/ghost fluid method for simulating turbulent atomization , 2008, J. Comput. Phys..

[21]  Song Jiang,et al.  A remapping-free, efficient Riemann-solvers based, ALE method for multi-material fluids with general EOS , 2013 .

[22]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[23]  Hong Yi,et al.  A survey of the marching cubes algorithm , 2006, Comput. Graph..

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

[25]  S. Osher,et al.  Upwind difference schemes for hyperbolic systems of conservation laws , 1982 .

[26]  Li Yuan,et al.  An Artificial Compressibility Method for 3D Phase-Field Model and its Application to Two-Phase Flows , 2017 .

[27]  Barna L. Bihari,et al.  Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I , 1997, SIAM J. Sci. Comput..

[28]  E. Feireisl,et al.  ANALYSIS OF A PHASE-FIELD MODEL FOR TWO-PHASE COMPRESSIBLE FLUIDS , 2010 .

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