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Adaptive and recursive time relaxed monte carlo methods for rarefied gas dynamics

Stefano Trazzi ; Lorenzo Pareschi ; Bernt Wennberg (Institutionen för matematiska vetenskaper, matematik)
SIAM Journal on Scientific Computing (1064-8275). Vol. 31 (2009), 2, p. 1379-1398.
[Artikel, refereegranskad vetenskaplig]

Recently a new class of Monte Carlo methods, called time relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes has been introduced [L. Pareschi and G. Russo, SIAM J. Sci. Comput., 23 (2001), pp. 1253–1273]. A generalized Wild sum expansion of the solution is the basis of the simulation schemes. After a splitting of the equation, the time discretization of the collision step is obtained from the Wild sum expansion of the solution by replacing high order terms in the expansion with the equilibrium Maxwellian distribution; in this way speed-up of the methods close to fluid regimes is obtained by efficiently thermalizing particles close to the equilibrium state. In this work we present an improvement of such methods which allows us to obtain an effective uniform accuracy in time without any restriction on the time step and subsequent increase of the computational cost. The main ingredient of the new algorithms is recursivity [L. Pareschi and B. Wennberg, Monte Carlo Methods Appl., 7 (2001), pp. 349–358]. Several techniques can be used to truncate the recursive trees generated by the schemes without degrading the accuracy of the numerical solution. Techniques based on adaptive strategies are presented. Numerical results emphasize the gain of efficiency of the present simulation schemes with respect to standard DSMC (direct simulation Monte Carlo) methods.

Nyckelord: Boltzmann equation, Monte Carlo methods, time relaxed schemes, fluid dynamic limit, stiff systems, recursive algorithms



Denna post skapades 2009-01-16. Senast ändrad 2016-07-11.
CPL Pubid: 88218

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur