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Talk Abstract
Uniformly Accurate Monte Carlo Methods for the Boltzmann Equation

Lorenzo Pareschi
Mathematics Department
University of Ferrara

For the Boltzmann equation, we formulate new Monte Carlo methods, that are robust in the fluid dynamic limit. The methods are based on an analytic representation of the solution over a single time step and involves implicit time differencing derived from a suitable power series expansion of the solution (a generalized Wild expansion). A class of unconditionally stable and explicitly implementable numerical schemes is obtained by relaxing the the high order terms in the expansion to the equilibrium Maxwellian distribution. Computational simulations by the new Time Relaxed Monte Carlo (TRMC) methods are presented here for the Variable Hard Sphere model. Comparison to exact solutions and to Direct Simulation Monte Carlo (DSMC) computations show the robustness and the efficiency of the new methods.

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