The FLAMEX Solver - Revision history

Yd at 17:01, 23 July 2023

2023-07-23T17:01:48Z

Yd at 17:00, 23 July 2023

2023-07-23T17:00:18Z

Yd: /* Evolution Equation Modeling for wrinkled fronts */

2016-04-18T20:20:28Z

‎Evolution Equation Modeling for wrinkled fronts

Yd: /* Main features of the EEM Module */

2016-04-08T16:26:56Z

‎Main features of the EEM Module

Yd: /* Evolution Equation Modeling for wrinkled fronts */

2016-04-08T16:25:48Z

‎Evolution Equation Modeling for wrinkled fronts

Yd: /* Module for percolating fronts PF */

2016-04-07T20:19:58Z

‎Module for percolating fronts PF

Yd: /* Participants */

2016-04-07T19:37:10Z

‎Participants

Yd: /* Module for percolating fronts PF */

2016-04-07T19:36:18Z

‎Module for percolating fronts PF

Yd at 19:32, 7 April 2016

2016-04-07T19:32:06Z

Yd at 19:28, 7 April 2016

2016-04-07T19:28:03Z

@@ Line 69: / Line 69: @@
 {| class="wikitable" style="margin: 1em auto 1em auto;"
-|{{#widget:YouTube|id=kSwhon6gQis|width=300|height=250}}
+|{{#widget:YouTube|id=kSwhon6gQis  |width=300 |height=250}}
-|{{#widget:YouTube|id=YxCRj6N7qY8|width=400|height=250}}
+|{{#widget:YouTube|id=YxCRj6N7qY8 |width=400 |height=250}}
 |}
 LEFT : FD DNS of a single-channel flame, showing pulsating instabilities (iso-temperature). A layer of heated unburnt material is formed then very quickly ‘shaved’ by a secondary channel-flame. This may even take place on top of the secondary flames themselves.

@@ Line 69: / Line 69: @@
 {| class="wikitable" style="margin: 1em auto 1em auto;"
-|{{#widget:YouTube|id=lyckMK-45jM|width=300|height=250}}
+|{{#widget:YouTube|id=kSwhon6gQis|width=300|height=250}}
 |{{#widget:YouTube|id=YxCRj6N7qY8|width=400|height=250}}
 |}

@@ Line 13: / Line 13: @@
 when the density contrast <math> \alpha </math> between 'hot' and 'cold' fluids is asymptotically small.
-* This Sivashinsky-type perturbative approach leads to non-linear non-local Evolution Equations.  At first (and second) order in <math> \alpha </math>, and 1st order in time,  the building terms in the EE  corresponds to a clearly identified phenomenon, like Landau-Darrieus hydrodynamic instability, Huygens-type propagation and curvature thermo-diffusive contribution.
+* This Sivashinsky-type perturbative approach leads to non-linear non-local Evolution Equations.  At first (and second) order in <math> \alpha </math>, and 1st order in time,  each building-block term in the EE  corresponds to a clearly identified phenomenon, like Landau-Darrieus hydrodynamic instability, Huygens-type propagation and curvature thermo-diffusive contribution.
 * FLAMEX is made of a suite of solvers, able to compute

@@ Line 21: / Line 21: @@
 ==Main features of the EEM Module==
-* Solving first-order or second order EE in the Fourier or Fourier-Legendre basis.
+* Solving first-order or second-order in time 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)
+* 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, tangential velocity, gravity effects...
-* Laminar or turbulent configurations (EE with additive noise, e.g. Passot-Pouquet, Kraichnan-Celik, Von Karman/Pao or 'DNS turbulence')
+* Laminar or turbulent configurations (EE with additive noise, e.g. Passot-Pouquet, Kraichnan-Celik, Von Karman/Pao or 'DNS turbulence').
 {| class="wikitable"
 |+ Examples of first-order in time obtained EEM: for 2D planar, 3D planar, or 3D expanding fronts

@@ Line 7: / Line 7: @@
 ==Evolution Equation Modeling for wrinkled fronts==
-For propagating fronts, considered as density surface discontinuities, a class of EEM (Evolution Equation Modeling) can be derived by analytically solving the set of
+*For propagating fronts, considered as density surface discontinuities, a class of EEM (Evolution Equation Modeling) can be derived by analytically solving the set of
-* Euler equations
+** Euler equations
-* Rankine-Hugoniot jump relationships
+** Rankine-Hugoniot jump relationships
-* a local kinematic relation defining the local front velocity (possibly depending on  local curvature).
+** a local kinematic relation defining the local front velocity (possibly depending on  local curvature).
-when the density contrast between 'hot' and 'cold' fluids is asymptotically small.
+when the density contrast <math> \alpha </math> 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.
+* This Sivashinsky-type perturbative approach leads to non-linear non-local Evolution Equations.  At first (and second) order in <math> \alpha </math>, and 1st order in time,  the building terms in the EE  corresponds to a clearly identified phenomenon, like Landau-Darrieus hydrodynamic instability, Huygens-type propagation and curvature thermo-diffusive contribution.
-FLAMEX is a suite of solvers, able to compute
+* FLAMEX is made of a suite of solvers, able to compute
-* EEM: high accuracy solutions to asymptotic expansion based evolution equations, of 1rt or 2nd order in time for wrinkled propagating fronts;
+** EEM: high accuracy solutions to asymptotic expansion based evolution equations, of 1rt or 2nd order in time for wrinkled propagating fronts;
-* FB: integro-differential evolution equations for flame-balls;
+** FB: integro-differential stochastic evolution equations for flame-balls;
-* PF: modeling and resolution of percolating fronts in disordered pre-mixtures.
+** PF: modeling and resolution of percolating fronts in disordered pre-mixtures.
 ==Main features of the EEM Module==

@@ Line 76: / Line 76: @@
 RIGHT : Numerical Simulation of the large-scale propagation (percolation) of a reacting front in non-diffusing disordered pre-mixtures (as a network collection of single-channel flames). The density of passing links fraction is increased from <math>p=0.51</math> to <math>p=0.8</math>.
-More details in  [http://dx.doi.org/10.1080/13647830802043978].
+<!--foo More details in  [http://dx.doi.org/10.1080/13647830802043978].-->
 == Participants ==
 Guy Joulin,  Rui Rego, Olivier Esnault, Gaël Boury, Eric Albin, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji, Yves D'Angelo.

← Older revision		Revision as of 19:37, 7 April 2016
Line 79:		Line 79:

	== Participants ==		== Participants ==
−	~~Yves D'Angelo,~~ Guy Joulin, ~~Eric Albin,~~ Rui Rego, Olivier Esnault, Gaël Boury, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji.	+	Guy Joulin, Rui Rego, Olivier Esnault, Gaël Boury, Eric Albin, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji, Yves D'Angelo.

@@ Line 5: / Line 5: @@
 Solving Asymptotics-based Evolution Equations and networks !
 ==Evolution Equation Modeling for wrinkled fronts==
@@ Line 16: / Line 15: @@
 This Sivashinsky-type perturbative approach leads to non-linear non-local EE, with easily identified meaningful terms.
-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.
+FLAMEX is a suite of solvers, able to compute
-== Main features of the EEM Module==
+==Main features of the EEM Module==
 * 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)
@@ Line 57: / Line 59: @@
 <center>System of equations, integro-differential evolution equation and sample results of FB radius dynamics</center>
 In solid-like pre-mixtures,  when the initial reactant content and/or reactivity are maxima along the axis of straight channels, curved flames are able to propagate under conditions.  Such individual channels (and the conditions for propagation) can be lumped as building blocks of a larger percolation network.

@@ Line 4: / Line 4: @@
-Solving Asymptotics-based Evolution Equations !
+Solving Asymptotics-based Evolution Equations and networks !
@@ Line 29: / Line 29: @@
 |}
-== Sample Results for EEM ==
+== Sample Results of the EEM module==
-We show below a short gallery of pictures obtained using the FLAMEX solver.
+We show below a short gallery of pictures obtained using the EEM module of the FLAMEX solver.
 {| class="wikitable"
 |+ Sample results for 3D planar fronts
@@ Line 43: / Line 43: @@
 * More details (and comparisons with experimental results) in [http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.018], [http://dx.doi.org/10.1016/j.combustflame.2011.12.019]
-==Modules for asymptotic modeling of Flame-Balls==
 Some modules of FLAMEX have 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 <math>g(t)</math>.
+Using a Batchelor approximation for the surrounding Lagrangian flow and high activation energy asymptotics, we derived a nonlinear forced (stochastic) integro-differential equation for the current FB radius. This gives access to the FB response to the ambiant Lagrangian rate-of-strain tensor <math>g(t)</math>.
 For a diagonal <math>g(t)</math> deduced from random Markov processes of the Ornstein-Uhlenbeck type,
 or linearly filtered versions thereof, extensive numerical simulations and approximate theoretical analyses agree that
@@ Line 55: / Line 57: @@
 <center>System of equations, integro-differential evolution equation and sample results of FB radius dynamics</center>
-==Modules for percolating fronts==
+==Module for percolating fronts PF==
 In solid-like pre-mixtures,  when the initial reactant content and/or reactivity are maxima along the axis of straight channels, curved flames are able to propagate under conditions.  Such individual channels (and the conditions for propagation) can be lumped as building blocks of a larger percolation network.