Geodesic
Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows
Y-Y Liu1 ; J. Xin2 ; Y. Yu2
1 Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan
2 Department of Mathematics, University of California, Irvine, CA 92697, USA
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 198-205.

Voir la notice de l'article provenant de la source EDP Sciences

We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The curvature-strain G-equations are also non-convex with degenerate diffusion. The computation is based on monotone finite difference discretization and weighted essentially nonoscillatory (WENO) methods. We found that the large time front speeds lock into the frequency of time periodic cellular flows in curvature-strain G-equations similar to what occurs in the basic inviscid G-equation. However, such frequency locking phenomenon disappears in viscous G-equation, and in the inviscid G-equation if time periodic oscillation of the cellular flow is replaced by time stochastic oscillation.
DOI : 10.1051/mmnp/20138312

Y-Y Liu 1 ; J. Xin 2 ; Y. Yu 2

1 Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan
2 Department of Mathematics, University of California, Irvine, CA 92697, USA 
@article{MMNP_2013_8_3_a11,
     author = {Y-Y Liu and J. Xin and Y. Yu},
     title = {Turbulent {Flame} {Speeds} of {G-equation} {Models} in {Unsteady} {Cellular} {Flows}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {198--205},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2013},
     doi = {10.1051/mmnp/20138312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138312/}
}
TY  - JOUR
AU  - Y-Y Liu
AU  - J. Xin
AU  - Y. Yu
TI  - Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows
JO  - Mathematical modelling of natural phenomena
PY  - 2013
SP  - 198
EP  - 205
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138312/
DO  - 10.1051/mmnp/20138312
LA  - en
ID  - MMNP_2013_8_3_a11
ER  - 
%0 Journal Article
%A Y-Y Liu
%A J. Xin
%A Y. Yu
%T Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows
%J Mathematical modelling of natural phenomena
%D 2013
%P 198-205
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138312/
%R 10.1051/mmnp/20138312
%G en
%F MMNP_2013_8_3_a11
Y-Y Liu; J. Xin; Y. Yu. Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 198-205. doi : 10.1051/mmnp/20138312. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138312/

[1] M. Abel, M. Cencini, D. Vergni, A. Vulpiani Chaos 2002 481 488

[2] M. Cencini, A. Torcini, D. Vergni, A. Vulpiani Phys. Fluids 2003 679 688

[3] P. Cardaliaguet, J. Nolen, P. E. Souganidis Arch. Rational Mech. Analysis 2011 527 561

[4] B. Denet Combust. Theory Model. 1999 585 589

[5] B. Khouider, A. Bourlioux, A. Majda Combust. Theory Model. 2001 295 318

[6] J. Nolen, J. Xin SIAM J. Multiscale Modeling and Simulation 2003 554 570

[7] J. Nolen, J. Xin Ann Inst. H. Poincaré, Analyse Non Lineaire 2009 815 839

[8] P. Cardaliaguet, P. E. Souganidis. Homogenization and Enhancement of the G-equation in Random Environments. Comm. Pure Appl. Math, to appear.

[9] Y.-Y. Liu, J. Xin, Y. Yu Arch. Rational Mech. Analysis 2011 461 492

[10] Y.-Y. Liu, J. Xin, Y. Yu Physica D 2013 20 31

[11] J. Nolen, A. Novikov Comm. Math Sci. 2011 561 582

[12] J. Nolen, J. Xin Physica D 2008 3172 3177

[13] A. Oberman. Ph.D. thesis, University of Chicago, Chicago, IL, 2001.

[14] S. Osher, R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York, NY 2002.

[15] N. Peters. Turbulent Combustion. Cambridge University Press, 2000.

[16] P.D. Ronny Lecture Notes in Physics 1995 3 22

[17] F. Williams, Turbulent Combustion. The Mathematics of Combustion (J. Buckmaster, ed.), SIAM, Philadelphia (1985) 97-131.

[18] J. Xin SIAM Review 2000 161 230

[19] J. Xin. An Introduction to Fronts in Random Media. Surveys and Tutorials in the Applied Mathematical Sciences 5, Springer, 2009.

[20] J. Xin, Y. Yu Comm. Math Sci. 2010 1067 1078

Cité par Sources :