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[[File:Flamex.jpg|240px]] | [[File:Flamex.jpg|240px]] | ||
− | FLAMEX is a suite of solvers able to compute high accuracy solutions to | + | FLAMEX is a suite of solvers able to compute high accuracy solutions to asymptotic expansion based evolution equations (EE), of 1rt or 2nd order in time. <br/ > |
− | For propagating fronts, | + | For propagating fronts, considerd as density surface discontinuities, EEM (Evolution Equation Modeling) can be derived by analytically solving the set of |
* Euler equations | * Euler equations | ||
− | * Rankine-Hugoniot jump | + | * Rankine-Hugoniot jump relationships |
− | * | + | * a local kinematic relation defining the local front velocity (e.g. with respect to local curvature). |
when the density contrast between 'hot' and 'cold' fluids is asymptotically small. | when the density contrast between 'hot' and 'cold' fluids is asymptotically small. | ||
+ | |||
+ | This Sivashinsky-type perturbative approach leads to non-linear non-local EE, with easily identified meaningful terms. | ||
== Main features== | == Main features== |
Revision as of 15:48, 1 April 2016
Contents
The FLAMEX Solver
FLAMEX is a suite of solvers able to compute high accuracy solutions to asymptotic expansion based evolution equations (EE), of 1rt or 2nd order in time.
For propagating fronts, considerd as density surface discontinuities, EEM (Evolution Equation Modeling) can be derived by analytically solving the set of
- Euler equations
- Rankine-Hugoniot jump relationships
- a local kinematic relation defining the local front velocity (e.g. with respect to local curvature).
when the density contrast between 'hot' and 'cold' fluids is asymptotically small.
This Sivashinsky-type perturbative approach leads to non-linear non-local EE, with easily identified meaningful terms.
Main features
- Solving first-order or second order EE in the Fourier or Fourier-Legendre basis.
- Time resolution using ETDRK1 and 4, using contour integrals to avoid cancelation errors (Trefethen et al. 2005)
- EEM for 2D or 3D planar, 3D expanding/converging fronts, acoustics, fast-transients..
- Laminar or turbulent configurations (EE with additive noise, e.g. Passot-Pouquet, Kraichnan-Celik, Von Karman/Pao or 'DNS turbulence')
Sample Results
We show below a short gallery of pictures obtained using the FLAMEX solver.
Notice the 'soccer-ball' and 'cauliflower' aspects of the front, as described by Zel'dovitch in the 40's.
- See also some quantitative comparisons between FLAMEX and DNS (HALLEGRO) results at [1]
- More details (and comparisons with experimental results) in [2], [3]
Sub-module for asymptotic modeling of Flame-Balls
A sub-module of FLAMEX has been devoted to the numerical solution to flame-balls (FB) dynamics. Using a Batchelor approximation for the surrounding Lagrangian flow and high activation energy asymptotics, we derived a nonlinear forced (stochastic) integrodifferential equation for the current FB radius. This gives access to the FB response to the ambiant Lagrangian rate-of-strain tensor g(t). For a diagonal g(t) deduced from random Markov processes of the Ornstein- Uhlenbeck type, or linearly filtered versions thereof, extensive numerical simulations and approximate theoretical analyses agree that
- flame balls can definitely live for much longer than their time of spontaneous expansion/collapse;
- large enough values of t_life are compatible with Poisson statistics;
- the variations of with the characteristics of g(t) mirror the latter’s statistics, more precisely that of trace(g*g).
Participants
Yves D'Angelo, Guy Joulin, Eric Albin, Rui Rego, Gaël Boury, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji.