Invariant manifolds and lattice Boltzmann method for combustion

The lattice Boltzmann (LB) method is a rel- atively novel approach to numerical flow simulations, and recent studies have proved that it is highly competitive to traditional methods when simulating compressible and turbulent flows (in terms of accuracy and efficiency). Although this makes LB a good candidate for computing reactive flows, applications in this field are still limited by the stiffness of the governing equations and the large amount of fields to solve. In this sense, the present study intends to provide an effective tool for reactive flow simulations via the LB method

[1]  Santosh Ansumali,et al.  Minimal kinetic modeling of hydrodynamics , 2004 .

[2]  R. Borghi,et al.  Turbulent reactive flows , 1989 .

[3]  N. Peters,et al.  Reduced Kinetic Mechanisms for Applications in Combustion Systems , 1993 .

[4]  Robert W. Dibble,et al.  Combustion: Physical and Chemical Fundamentals, Modelling and Simulation, Experiments, Pollutant Formation , 1996 .

[5]  Qing Tang,et al.  A more accurate projection in the rate-controlled constrained-equilibrium method for dimension reduction of combustion chemistry , 2004 .

[6]  James C. Keck,et al.  Rate-controlled partial-equilibrium method for treating reacting gas mixtures , 1971 .

[7]  D. Martínez,et al.  On boundary conditions in lattice Boltzmann methods , 1996 .

[8]  Tamás Turányi,et al.  Mathematical Tools for the Construction, Investigation and Reduction of Combustion Mechanisms , 1998 .

[9]  R. Temam,et al.  Inertial manifolds and slow manifolds , 1991 .

[10]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[11]  Iliya V. Karlin,et al.  Method of invariant manifold for chemical kinetics , 2003 .

[12]  S. Lam,et al.  The CSP method for simplifying kinetics , 1994 .

[13]  Lev Ryashko,et al.  On exponentially attracting invariant manifolds of ODEs , 2003 .

[14]  C. Eckett,et al.  Numerical and analytical studies of the dynamics of gaseous detonations , 2001 .

[15]  U. Maas,et al.  A general algorithm for improving ILDMs , 2002 .

[16]  Invariant manifolds for dissipative systems , 2009 .

[17]  A. Gorban,et al.  Invariant Manifolds for Physical and Chemical Kinetics , 2005 .

[18]  Alexander N Gorban,et al.  Legendre integrators, post-processing and quasiequilibrium , 2003, cond-mat/0308488.

[19]  Stephen B. Pope.  Gibbs function continuation for the stable computation of chemical equilibrium , 2004 .

[20]  Sheng Chen,et al.  A simple lattice Boltzmann scheme for combustion simulation , 2008, Comput. Math. Appl..

[21]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[22]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[23]  Herschel Rabitz.  Chemical dynamics and kinetics phenomena as revealed by sensitivity analysis techniques , 1987 .

[24]  A. M. Lyapunov.  The general problem of the stability of motion , 1992 .

[25]  Iliya V. Karlin,et al.  Quasi-equilibrium grid algorithm: Geometric construction for model reduction , 2007, J. Comput. Phys..

[26]  M. Kramer,et al.  Sensitivity Analysis in Chemical Kinetics , 1983 .

[27]  Alexander N Gorban,et al.  Relaxational trajectories: global approximations , 1996 .

[28]  Ulrich Maas,et al.  Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space , 1992 .

[29]  Chuan Yi Tang,et al.  A 2.|E|-Bit Distributed Algorithm for the Directed Euler Trail Problem , 1993, Inf. Process. Lett..

[30]  Alexander N Gorban,et al.  Invariant grids for reaction kinetics , 2003 .

[31]  K. Boulouchos,et al.  Simulation of binary mixtures with the lattice Boltzman method. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Siegfried M. Rump,et al.  INTLAB - INTerval LABoratory , 1998, SCAN.