Heterogeneous multiscale methods for interface tracking of combustion fronts

Multiscale Modeling and Simulation

Volumn 5, Issue 2, 2006, Pages 532-563

  Sun, Yi ^a   Engquist, Bjorn ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Combustion; Euler equations; Heterogeneous multiscale methods; Interface tracking; Phase field method

Indexed keywords

COMPUTER SIMULATION; EULER EQUATIONS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS;

HETEROGENEOUS MULTISCALE METHODS; INTERFACE TRACKING; PHASE FIELD METHOD;

COMBUSTION;

EID: 34250345318     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/050624844     Document Type: Article

References (34)

1. A. ABDULLE AND W. E, Finite difference heterogeneous multi-scale method for homogenization problems, J. Comput. Phys., 191 (2003), pp. 18-39.
2. W. BAO AND S. JIN, The random projection method for hyperbolic conservation laws with stiff reaction terms, J. Comput. Phys., 163 (2000), pp. 216-248.
3. W. BAO AND S. JIN, The random projection method for stiff multispecies detonation capturing, J. Comput. Phys., 178 (2002), pp. 37-57.
4. M. J. BERGER AND R. J. LEVEQUE, Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems, SIAM J. Numer. Anal., 35 (1998), pp. 2298-2316.
5. M. J. BERGER AND J. OLIGER, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), pp. 484-512.
6. A. BOURLIOUX, Numerical Study of Unstable Detonations, Ph.D. thesis, Princeton University, Princeton, NJ, 1991.
7. L. T. CHENG AND W. E, The heterogeneous multi-scale method for interface dynamics, in Recent Advances in Scientific Computing and Partial Differential Equations, Contemp. Math. 330, AMS, Providence, RI, 2003, pp. 43-53.
8. P. COLELLA, A. MAJDA, AND V. ROYTBURD, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 1059-1080.
9. P. COLELLA AND P. WOODWARD, The piecewise-parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys., 54 (1984), pp. 174-201.
10. W. E, Analysis of the heterogeneous multiscale method for ordinary differential equations, Commun. Math. Sci., 1 (2003), pp. 423-436.
11. W. E AND B. ENGQUIST, The heterogeneous multiscale methods, Commun. Math. Sci., 1 (2003), pp. 87-132.
12. W. E AND B. ENGQUIST, The heterogeneous multi-scale method for homogenization problems, in Multiscale Methods in Science and Engineering, Lect. Notes Comput. Sci. Eng. 44, Springer, Berlin, 2005, pp. 89-110.
13. W. E, B. ENGQUIST, AND Z. HUANG, Heterogeneous multi-scale method - a general methodology for multi-scale modeling, Phys. Rev. B, 67 (2003), 092101.
14. B. ENGQUIST AND S. OSHER, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp., 34 (1980), pp. 45-75.
15. B. ENGQUIST AND R. TSAI, Heterogeneous multiscale methods for stiff ordinary differential equations, Math. Comp., 74 (2005), pp. 1707-1742.
16. H. FAN AND S. JIN, Front motion in multi-dimensional viscous conservation laws with stiff source terms driven by mean curvature and front thickness, Quart. Appl. Math., 61 (2003), pp. 701-721.
17. I. GLASSMAN, Combustion, Academic Press, San Diego, CA, 1987.
18. J. GLIMM, J. W. GROVE, X. L. Li, W. OH, AND D. H. SHARP, A critical analysis of Rayleigh-Taylor growth rates, J. Comput. Phys., 169 (2001), pp. 652-677.
19. C. HELZEL, R. J. LEVEQUE, AND O. WARNECKE, A modified fractional step method for the accurate approximation of detonation waves, SIAM J. Sci. Comput., 22 (2000), pp. 1489-1510.
20. P. KLINGENSTEIN, Hyperbolic Conservation Laws with Stiff Source Terms: Errors in the Shock Location, ETH SAM Report 94-07, 1994, ETH Dissertation, ETH Zürich, Zürich, Switzerland, 1995.
21. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhäuser-Verlag, Boston, MA, 1990.
22. R. J. LEVEQUE AND H. C. YEE, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comput. Phys., 86 (1990), pp. 187-210.
23. R. J. LEVEQUE AND K.-M. SHYUE, One-dimensional front tracking based on high resolution wave propagation methods, SIAM J. Sci. Comput., 16 (1994), pp. 348-377.
24. T. LI, E. VANDEN-EIJNDEN, P. ZHANG, AND W. E, Stochastic models of polymeric fluids at small Deborah number, J. Non-Newtonian Fluid Mech., 121 (2004), pp. 117-125.
25. A. MAJDA, A qualitative model for dynamic combustion, SIAM J. Appl. Math., 41 (1981), pp. 70-93.
26. E. S. ORAN AND J. P. BORIS, Numerical Simulation of Reactive Flow, Elsevier, New York, 1987.
27. S. OSHER AND R. FEDKIW, Level Set Methods and Dynamic Implicit Surfaces, Springer, New York, 2003.
28. S. OSHER AND J. SETHIAN, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), pp. 12-49.
29. P. L. ROE, Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys., 43 (1981), pp. 357-372.
30. J. RUBINSTEIN, P. STERNBERG, AND J. B. KELLER, Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math., 49 (1989), pp. 116-133.
31. T. P. SCHULZE, P. SMEREKA, AND W. E, Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth J. Comput. Phys., 189 (2003), pp. 197-211.
32. B. SJÖGREEN AND B. ENGQUIST, Numerical approximation of hyperbolic conservation laws with stiff terms, in Hyperbolic Problems. Theory, Numerical Methods and Applications, Studentlitteratur, Chartwell-Bratt Ltd., Lund, Sweden, Bromley, UK, 1991, pp. 848-860.
33. A.-K. TORNBERG AND B. ENGQUIST, The segment projection method for interface tracking, Comm. Pure Appl. Math., 56 (2003), pp. 47-79.
34. G. TRYGGVASON, B. BRUNNER, A. ESMAELI, D. JURIC, N. AL-RAWAHI, W. TAUBER, J. HAN, S. NAS, AND Y.-J. JAN, A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169 (2001), pp. 708-759.