A conservative interface-interaction method for compressible multi-material flows

Abstract In this paper we develop a conservative interface-interaction method dedicated to simulating multiple compressible fluids with sharp interfaces. Numerical models for finite-volume cells cut by more than two material-interface are proposed. First, we simplify the interface interaction inside such a cell to avoid the need for explicit interface reconstruction and very complex flux calculation. Second, conservation is strictly preserved by an efficient conservation correction procedure for the cut cell. To improve robustness, a multi-material scale separation model is developed to remove consistently non-resolved interface scales. In addition, a multi-resolution method and a local time-stepping scheme are incorporated into the proposed multi-material method to speed up high-resolution simulations. Various numerical test cases, including the multi-material shock tube problem, inertial confinement fusion implosion, triple-point shock interaction and shock interaction with multi-material bubbles, show that the method is suitable for a wide range of complex compressible multi-material flows.

[1]  O. E. Bronson Messer,et al.  THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVA SIMULATED USING A 15 M⊙ PROGENITOR , 2015, 1505.05110.

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

[3]  Theo G. Theofanous,et al.  Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method , 2013, J. Comput. Phys..

[4]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[5]  N. Zabusky,et al.  Shock cavity implosion morphologies and vortical projectile generation in axisymmetric shock–spherical fast/slow bubble interactions , 1998, Journal of Fluid Mechanics.

[6]  Kai Schneider,et al.  An adaptive multiresolution scheme with local time stepping for evolutionary PDEs , 2008, J. Comput. Phys..

[7]  Marcus Herrmann,et al.  A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure , 2010, J. Comput. Phys..

[8]  Xiangyu Hu,et al.  An interface interaction method for compressible multifluids , 2004 .

[9]  R. Abgrall,et al.  A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows , 1999 .

[10]  Paul R. Woodward,et al.  Cross-code comparisons of mixing during the implosion of dense cylindrical and spherical shells , 2014, J. Comput. Phys..

[11]  Mark H. Anderson,et al.  A computational parameter study for the three-dimensional shock–bubble interaction , 2007, Journal of Fluid Mechanics.

[12]  Nikolaus A. Adams,et al.  Anti-diffusion interface sharpening technique for two-phase compressible flow simulations , 2012, J. Comput. Phys..

[13]  Mikhail J. Shashkov,et al.  Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods , 2014, J. Comput. Phys..

[14]  Jérôme Breil,et al.  A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction , 2010, J. Comput. Phys..

[15]  Tzanio V. Kolev,et al.  High-order curvilinear finite elements for axisymmetric Lagrangian hydrodynamics , 2013 .

[16]  Nikolaus A. Adams,et al.  Efficient formulation of scale separation for multi-scale modeling of interfacial flows , 2016, J. Comput. Phys..

[17]  Dimitris Drikakis,et al.  Mach number effects on shock-bubble interaction , 2001 .

[18]  Nikolaus A. Adams,et al.  High-resolution method for evolving complex interface networks , 2018, Comput. Phys. Commun..

[19]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

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

[21]  Marcus Herrmann,et al.  A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids , 2008, J. Comput. Phys..

[22]  G. Kreiss,et al.  A conservative level set method for two phase flow II , 2005, Journal of Computational Physics.

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

[24]  Kenneth A. Brakke,et al.  The Surface Evolver , 1992, Exp. Math..

[25]  Nikolaus A. Adams,et al.  A cut-cell finite volume - finite element coupling approach for fluid-structure interaction in compressible flow , 2015, J. Comput. Phys..

[26]  Jun-Hai Yong,et al.  Simulation of bubbles , 2006, SCA '06.

[27]  J. Haas,et al.  Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities , 1987, Journal of Fluid Mechanics.

[28]  Nikolaus A. Adams,et al.  Scale separation for multi-scale modeling of free-surface and two-phase flows with the conservative sharp interface method , 2015, J. Comput. Phys..

[29]  E. Toro,et al.  Restoration of the contact surface in the HLL-Riemann solver , 1994 .

[30]  David J. Benson,et al.  Volume of fluid interface reconstruction methods for multi - material problems , 2002 .

[31]  R. Bonazza,et al.  Shock-Bubble Interactions , 2011 .

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

[33]  A. Harten.  Multiresolution algorithms for the numerical solution of hyperbolic conservation laws , 2010 .

[34]  David P. Starinshak,et al.  A multimaterial extension to subzonal reconstruction , 2016, J. Comput. Phys..

[35]  Michael L. Gittings,et al.  Two- and Three-Dimensional Simulations of Asteroid Ocean Impacts , 2002 .

[36]  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..

[37]  Deliang Zhang,et al.  An improved CE/SE scheme for multi-material elastic–plastic flows and its applications , 2009 .

[38]  Nikolaus A. Adams,et al.  A Consistent Analytical Formulation for Volume Estimation of Geometries Enclosed by Implicitly Defined Surfaces , 2017, SIAM J. Sci. Comput..

[39]  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..

[40]  Olivier Roussel,et al.  A conservative fully adaptive multiresolution algorithm for parabolic PDEs , 2003 .

[41]  V A Thomas,et al.  Drive asymmetry and the origin of turbulence in an ICF implosion. , 2012, Physical review letters.

[42]  Mikhail J. Shashkov,et al.  Reconstruction of multi-material interfaces from moment data , 2008, J. Comput. Phys..

[43]  Theo G. Theofanous,et al.  Adaptive characteristics-based matching for compressible multifluid dynamics , 2006, J. Comput. Phys..

[44]  Xiangyu Y. Hu,et al.  High-order time-marching reinitialization for regional level-set functions , 2018, J. Comput. Phys..

[45]  Xianyi Zeng,et al.  A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian-Eulerian flow computations , 2014, J. Comput. Phys..

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

[47]  G. Iaccarino,et al.  Multi-scale modeling of compressible multi-fluid flows with conservative interface method , 2010 .

[48]  Keh-Ming Shyue,et al.  A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state , 2001 .

[49]  F. Kummer,et al.  Simple multidimensional integration of discontinuous functions with application to level set methods , 2012 .

[50]  Philip L. Roe,et al.  A new level set model for multimaterial flows , 2014, J. Comput. Phys..

[51]  Nikolaus A. Adams,et al.  On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow , 2009, J. Comput. Phys..