Free Access
Issue |
ESAIM: M2AN
Volume 41, Number 6, November-December 2007
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Page(s) | 1089 - 1123 | |
DOI | https://doi.org/10.1051/m2an:2007048 | |
Published online | 15 December 2007 |
- R. Abeyaratne and J. Knowles, Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114 (1991) 119–154. [CrossRef] [Google Scholar]
- R. Abgrall and S. Karni, Compressible multifluid flows. J. Comput. Phys. 169 (2001) 594–623. [CrossRef] [MathSciNet] [Google Scholar]
- R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186 (2003) 361–396. [CrossRef] [MathSciNet] [Google Scholar]
- T.D. Aslam, A level set algorithm for tracking discontinuities in hyperbolic conservation laws II: Systems of equations. J. Sci. Comput. 19 (2003) 37–62. [CrossRef] [MathSciNet] [Google Scholar]
- N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive travelling waves and kinetic relations. II. A hyperbolic-elliptic model of phase-transition dynamics. Proc. Roy. Soc. Edinburgh Sect. A 132A (2002) 1–21. [Google Scholar]
- S. Benzoni-Gavage, Stability of multi-dimensional phase transitions in a van der Waals fluid. Nonlinear Anal., Theory Methods Appl. 31 (1998) 243–263. [Google Scholar]
- C. Chalons, Transport-Equilibrium Schemes for Computing Nonclassical Shocks. I. Scalar Conservation Laws. Preprint, Laboratoire Jacques-Louis Lions (2005). [Google Scholar]
- C. Chalons and P.G. LeFloch, Computing undercompressive waves with the random choice scheme. Interfaces Free Bound. 5 (2003) 129–158. [CrossRef] [MathSciNet] [Google Scholar]
- R.M. Colombo and A. Corli, Continuous dependence in conservation laws with phase transitions. SIAM J. Math. Anal. 31 (1999) 34–62. [CrossRef] [MathSciNet] [Google Scholar]
- R.M. Colombo and A. Corli, Stability of the Riemann semigroup with respect to the kinetic condition. Quart. Appl. Math. 62 (2004) 541–551. [MathSciNet] [Google Scholar]
- C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Grundlehren der mathematischen Wisenschaften 325. Springer (2000). [Google Scholar]
- H. Fan and M. Slemrod, Dynamic flows with liquid/vapor phase transitions, in Handbook of mathematical fluid dynamics, Vol. I, North-Holland, Amsterdam (2002) 373–420. [Google Scholar]
- R.P. Fedkiw, T. Aslam, B. Merriman and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152 (1999) 457–492. [CrossRef] [MathSciNet] [Google Scholar]
- R.P. Fedkiw, T. Aslam and S. Xu, The ghost fluid method for deflagration and detonation discontinuities. J. Comput. Phys. 154 (1999) 393–427. [Google Scholar]
- E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Appl. Math. Sci. 118 Springer (1996). [Google Scholar]
- E. Godlewski and N. Seguin, The Riemann problem for a simple model of phase transition. Commun. Math. Sci. 4 (2006) 227–247. [MathSciNet] [Google Scholar]
- B. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations: strictly hyperbolic systems. SIAM J. Math. Anal. 31 (2000) 941–991. [Google Scholar]
- T.Y. Hou, P. Rosakis and P.G. LeFloch, A level-set approach to the computation of twinning and phase-transition dynamics. J. Comput. Phys. 150 (1999) 302–331. [CrossRef] [MathSciNet] [Google Scholar]
- M. Kac, G.E. Uhlenbeck and P.C. Hemmer, On the van der Waals theory of the vapor-liquid equilibrium. I. Discussion of a one-dimensional model. J. Math. Phys. 4 (1963) 216–228. [NASA ADS] [CrossRef] [Google Scholar]
- S. Karni and R. Abgrall, Ghost-Fluids for the Poor: A Single Fluid Algorithm for Multifluids, in Lecture Notes in Mathematics, Proceedings of the 10th International Conference on Hyperbolic problems, theory and numerics, Springer (2001) 293–302. [Google Scholar]
- O. Le Métayer, J. Massoni and R. Saurel, Modelling evaporation fronts with reactive Riemann solvers. J. Comput. Phys. 205 (2005) 567–610. [CrossRef] [MathSciNet] [Google Scholar]
- P.G. LeFloch, Propagating phase boundaries: Formulation of the problem and existence via the Glimm method. Arch. Ration. Mech. Anal. 123 (1993) 153–197. [Google Scholar]
- P.G. LeFloch, Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves. Lectures in Mathematics. ETH Zürich, Birkhäuser (2002). [Google Scholar]
- P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transitions. Proc. Royal Soc. Edinburgh A 131A (2001) 1–39. [Google Scholar]
- P.G. LeFloch, J.M. Mercier and C. Rohde, Fully discrete, entropy conservative schemes of arbitrary order. SIAM J. Numer. Anal. 40 (2002) 1968–1992. [Google Scholar]
- T.G. Liu, B.C. Khoo and K.S. Yeo, Ghost fluid method for strong impacting on material interfaces. J. Comput. Phys. 190 (2003) 651–681. [CrossRef] [Google Scholar]
- C. Merkle, Dynamical Phase Transitions in Compressible Media. Doctoral dissertation, Albert-Ludwigs-Universität Freiburg (2006) http://www.freidok.uni-freiburg.de/volltexte/2674/. [Google Scholar]
- C. Merkle and C. Rohde, Computation of dynamical phase transitions in solids. Appl. Numer. Math. 56 (2006) 1450–1463. [CrossRef] [MathSciNet] [Google Scholar]
- W. Mulder, S. Osher and J. Sethian, Computing interface motion in compressible gas dynamics. J. Comput. Phys. 100 (1992) 209–228. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- S. Müller and A. Voß, The Riemann problem for the Euler equations with nonconvex and nonsmooth equation of state: construction of wave curves. SIAM J. Sci. Comput. 28 (1992) 651–681. [Google Scholar]
- S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Appl. Math. Sci. 153. Springer (2003). [Google Scholar]
- S. Osher and J. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12–49. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- S. Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28 (1991) 907–922. [CrossRef] [MathSciNet] [Google Scholar]
- D. Peng, B. Merriman, S. Osher, H.K. Zhao and M. Kang, A PDE-based fast local level set method. J. Comput. Phys. 155 (1999) 410–438. [CrossRef] [MathSciNet] [Google Scholar]
- G. Russo and P. Smereka, A remark on computing distance functions. J. Comput. Phys. 163 (2000) 51–67. [CrossRef] [MathSciNet] [Google Scholar]
- D. Serre, Systems of Conservation Laws 1. Cambridge University Press (1999). [Google Scholar]
- M. Sussman, P. Smereka and S. Osher, A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1994) 146–154. [Google Scholar]
- E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA Isaac Newton Institute for Mathematical Sciences (2003). [Google Scholar]
- L. Truskinovsky, Kinks versus Shocks, in Shock induced transitions and phase structures in general media, Springer, New York (1993) 185–229. [Google Scholar]
- L. Truskinovsky and A. Vainchtein, Explicit kinetic relation from “first principles”, in Mechanics of material forces 11, Advances in Mechanics and Mathematics, P. Steinmann and G.A. Maugin (Eds.), Springer (2005) 43–50. [Google Scholar]
- X. Zhong, T.Y. Hou and P.G. LeFloch, Computational method for propagating phase boundaries. J. Comput. Phys. 124 (1996) 192–216. [CrossRef] [MathSciNet] [Google Scholar]
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