1Université Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France, 2Université Paris Est, Laboratoire d’hydraulique Saint-Venant (Ecole des Ponts ParisTech – EDF R& D – CEREMA), 6 quai Watier, 78401 Chatou, France 3Laboratoire de Mathématiques, CNRS et Université de Paris-Sud, 91405 Orsay Cedex, France,
ESAIM. Proceedings, Tome 48 (2015), pp. 308-320
Cet article a éte moissonné depuis la source EDP Sciences
We perform numerical simulations in the one-dimensional torus for the first order Burgers equation forced by a stochastic source term with zero spatial integral. We suppose that this source term is a white noise in time, and consider various regularities in space. For the numerical tests, we apply a finite volume scheme combining the Godunov numerical flux with the Euler-Maruyama integrator in time. Our Monte-Carlo simulations are analyzed in bounded time intervals as well as in the large time limit, for various regularities in space. The empirical mean always converges to the space-average of the (deterministic) initial condition as t → ∞, just as the solution of the deterministic problem without source term, even if the stochastic source term is very rough. The empirical variance also stablizes for large time, towards a limit which depends on the space regularity and on the intensity of the noise.
1
Université Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France,
2
Université Paris Est, Laboratoire d’hydraulique Saint-Venant (Ecole des Ponts ParisTech – EDF R& D – CEREMA), 6 quai Watier, 78401 Chatou, France
3
Laboratoire de Mathématiques, CNRS et Université de Paris-Sud, 91405 Orsay Cedex, France,
@article{EP_2015_48_a14,
author = {Emmanuel Audusse and S\'ebastien Boyaval and Yueyuan Gao and Danielle Hilhorst},
title = {Numerical simulations of the inviscid burgers equation with periodic boundary conditions and stochastic forcing},
journal = {ESAIM. Proceedings},
pages = {308--320},
year = {2015},
volume = {48},
doi = {10.1051/proc/201448014},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201448014/}
}
TY - JOUR
AU - Emmanuel Audusse
AU - Sébastien Boyaval
AU - Yueyuan Gao
AU - Danielle Hilhorst
TI - Numerical simulations of the inviscid burgers equation with periodic boundary conditions and stochastic forcing
JO - ESAIM. Proceedings
PY - 2015
SP - 308
EP - 320
VL - 48
UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201448014/
DO - 10.1051/proc/201448014
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%A Emmanuel Audusse
%A Sébastien Boyaval
%A Yueyuan Gao
%A Danielle Hilhorst
%T Numerical simulations of the inviscid burgers equation with periodic boundary conditions and stochastic forcing
%J ESAIM. Proceedings
%D 2015
%P 308-320
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%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201448014/
%R 10.1051/proc/201448014
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%F EP_2015_48_a14
Emmanuel Audusse; Sébastien Boyaval; Yueyuan Gao; Danielle Hilhorst. Numerical simulations of the inviscid burgers equation with periodic boundary conditions and stochastic forcing. ESAIM. Proceedings, Tome 48 (2015), pp. 308-320. doi: 10.1051/proc/201448014
