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Analytic expressions of the solutions of advection-diffusion problems in 1D with discontinuous coefficients

Abstract : In this article, we provide a method to compute analytic expressions of the resolvent kernel of differential operators of the diffusion type with discontinuous coefficients in one dimension. Then we apply it when the coefficients are piecewise constant. We also perform the Laplace inversion of the resolvent kernel to obtain expressions of the transition density functions or fundamental solutions. We show how these explicit formula are useful to simulate advection-diffusion problems using particle tracking techniques
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https://hal.inria.fr/hal-01644270
Contributor : Antoine Lejay Connect in order to contact the contributor
Submitted on : Tuesday, February 19, 2019 - 5:18:43 PM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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Antoine Lejay, Lionel Lenôtre, Géraldine Pichot. Analytic expressions of the solutions of advection-diffusion problems in 1D with discontinuous coefficients. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2019, 79 (5), pp.1823-1849. ⟨10.1137/18M1164500⟩. ⟨hal-01644270v2⟩

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