Monte Carlo simulations of the randomly forced Burgers equationP. Düben1, D. Homeier1, K. Jansen2, D. Mesterhazy3, G. Münster1 and C. Urbach3
1 Westfälische Wilhelms-Universität Münster - Schlossplatz 2, D-48149 Münster, Germany, EU
2 DESY - Platanenallee 6, D-15738 Zeuthen, Germany, EU
3 Humboldt-Universität zu Berlin - Unter den Linden 6, D-10099 Berlin, Germany, EU
received 29 September 2008; accepted in final form 9 October 2008; published November 2008
published online 28 October 2008
The behaviour of the one-dimensional random-forced Burgers equation is investigated in the path integral formalism, using a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero-viscosity limit (Hopf equation) eventually leads to constraints on lattice parameters, required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained.
02.70.Uu - Applications of Monte Carlo methods.
05.20.Jj - Statistical mechanics of classical fluids.
47.40.Nm - Shock wave interactions and shock effects.
© EPLA 2008