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Books Year : 2015

NUMERICAL SIMULATIONS OF THE PERIODIC INVISCID BURGERS EQUATION WITH STOCHASTIC FORCING

Emmanuel Audusse
Yueyuan Gao
  • Function : Scientific advisor
  • PersonId : 954152
Danielle Hilhorst

Abstract

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 egularities 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.
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Dates and versions

hal-00962213 , version 1 (24-03-2014)
hal-00962213 , version 2 (27-06-2014)

Identifiers

  • HAL Id : hal-00962213 , version 2

Cite

Emmanuel Audusse, Sébastien Boyaval, Yueyuan Gao, Danielle Hilhorst (Dir.). NUMERICAL SIMULATIONS OF THE PERIODIC INVISCID BURGERS EQUATION WITH STOCHASTIC FORCING. 48, pp.308-320, 2015, ESAIM: Proceedings and Surveys. ⟨hal-00962213v2⟩
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