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With the name of a city famous for casinos and gambling, the Monte Carlo (MC) method owes its name to the random numbers that are used to describe possible outcomes of particle trajectories. Contrary to fluid methods, which describe local properties with differential changes approximated on a mesh, particle methods use the evolution of a large number of samplers to relate the motion at the microscopic scale with statistical changes at the macroscopic scale. The random nature of the method draws on results from the stochastic calculus that will be quickly summarized first for readers who are not at all familiar with this topic.

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