Simulating diffusion processes in discontinuous media: Benchmark tests

Abstract : We present several benchmark tests for Monte Carlo methods simulating diffusion in one-dimensional discontinuous media. These benchmark tests aim at studying the potential bias of the schemes and their impact on the estimation of micro-or macroscopic quantities (repartition of masses, fluxes, mean residence time,. . .). These benchmark tests are backed by a statistical analysis to filter out the bias from the unavoidable Monte Carlo error. We apply them on four different algorithms. The results of the numerical tests give a valuable insight of the fine behavior of these schemes, as well as rules to choose between them.
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https://hal.inria.fr/hal-01003853
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Antoine Lejay, Géraldine Pichot. Simulating diffusion processes in discontinuous media: Benchmark tests. Journal of Computational Physics, Elsevier, 2016, 314, pp.384 - 413. ⟨10.1016/j.jcp.2016.03.003⟩. ⟨hal-01003853v4⟩

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