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NUMERICAL SIMULATIONS OF THE PERIODIC INVISCID BURGERS EQUATION WITH STOCHASTIC FORCING

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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https://hal.archives-ouvertes.fr/hal-00962213
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Submitted on : Friday, June 27, 2014 - 9:39:25 AM
Last modification on : Sunday, June 26, 2022 - 12:01:36 PM
Long-term archiving on: : Saturday, September 27, 2014 - 10:50:27 AM

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  • HAL Id : hal-00962213, version 2

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

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