The Heterogeneous Multiscale Methods with Application to Combustion

The framework of the heterogeneous multiscale methods (HMM) is briefly reviewed. Both the original HMM and the seamless HMM are discussed. Applications to interface capturing and flame front tracking are presented.

[1]  B. Engquist,et al.  The segment projection method for interface tracking , 2003 .

[2]  Weiqing Ren,et al.  Seamless multiscale modeling of complex fluids using fiber bundle dynamics , 2007 .

[3]  Eric Vanden-Eijnden,et al.  ON HMM-like integrators and projective integration methods for systems with multiple time scales , 2007 .

[4]  Olof Runborg,et al.  Multi-scale methods for wave propagation in heterogeneous media , 2009, 0911.2638.

[5]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[6]  S. Osher,et al.  Stable and entropy satisfying approximations for transonic flow calculations , 1980 .

[7]  E Weinan,et al.  A general strategy for designing seamless multiscale methods , 2009, J. Comput. Phys..

[8]  A. Brandt.  Multiscale Scientific Computation: Review 2001 , 2002 .

[9]  Eric Vanden Eijnden.  Numerical techniques for multi-scale dynamical systems with stochastic effects , 2003 .

[10]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[11]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[12]  Andrew J. Majda,et al.  Qualitative model for dynamic combustion , 1981 .

[13]  Eric Vanden-Eijnden,et al.  A computational strategy for multiscale systems with applications to Lorenz 96 model , 2004 .

[14]  E Weinan,et al.  Multi-scale Modeling and Computation , 2003 .

[15]  E Weinan,et al.  Heterogeneous multiscale methods: A review , 2007 .

[16]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[17]  Randall J. LeVeque,et al.  A study of numerical methods for hyperbolic conservation laws with stiff source terms , 1990 .

[18]  E. Weinan,et al.  Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics , 2005 .

[19]  E Weinan,et al.  Seamless multiscale modeling via dynamics on fiber bundles , 2007 .

[20]  Björn Engquist,et al.  Heterogeneous multiscale methods for stiff ordinary differential equations , 2005, Math. Comput..

[21]  P. Colella,et al.  Theoretical and numerical structure for reacting shock waves , 1986 .

[22]  E Weinan,et al.  The Heterognous Multiscale Methods , 2003 .

[23]  David H. Sharp,et al.  Front Tracking Applied to Rayleigh–Taylor Instability , 1986 .

[24]  S. Y. Cheng,et al.  Recent advances in scientific computing and partial differential equations : international conference on the occasion of Stanley Osher's 60th birthday, December 12-15, 2002, Hong Kong Baptist University, Hong Kong , 2003 .

[25]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[26]  Eric Vanden-Eijnden,et al.  NUMERICAL TECHNIQUES FOR MULTI-SCALE DYNAMICAL SYSTEMS WITH STOCHASTIC EFFECTS ⁄ , 2003 .

[27]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[28]  C. W. Gear,et al.  Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis , 2003 .

[29]  Yi Sun,et al.  Heterogeneous Multiscale Methods for Interface Tracking of Combustion Fronts , 2006, Multiscale Model. Simul..

[30]  Elaine S. Oran,et al.  Numerical Simulation of Reactive Flow , 1987 .

[31]  Haitao Fan,et al.  Front motion in multi-dimensional viscous conservation laws with stiff source terms driven by mean curvature and variation of front thickness , 2003 .

[32]  E. Weinan.  Analysis of the heterogeneous multiscale method for ordinary differential equations , 2003 .

[33]  Randall J. LeVeque,et al.  A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves , 2000, SIAM J. Sci. Comput..