A high-order semi-Lagrangian method for the consistent Monte-Carlo solution of stochastic Lagrangian drift–diffusion models coupled with Eulerian discontinuous spectral element method
نویسندگان
چکیده
The explicit semi-Lagrangian method for solution of Lagrangian transport equations as developed in Natarajan and Jacobs (2020) is adopted the stochastic differential that consistent with Discontinuous Spectral Element Method (DSEM) approximations Eulerian conservation laws. extends favorable properties DSEM include its high-order accuracy, local boundary fitted high performance on parallel platforms concurrent Monte-Carlo, a class time-dependent problems can be described by coupled Eulerian–Lagrangian formulations. Such formulations probabilistic models used simulation chemically reacting turbulent flows or particle-laden flows. Consistent an explicit, discretization, seeds particles at Gauss quadrature collocation nodes within spectral element. are integrated explicitly time according to drift velocity Wiener increment forcing form nodal basis advected interpolant. This interpolant mapped back fashion points through least squares fit using constraints element values. Stochastic Monte-Carlo samples averaged element-wise nodes. stable step sufficiently small prevent from leaving element’s bounds. hence does not have grid complexity, parallelization challenges commonly particle solvers particle-mesh methods Formal proof presented algorithm evolves Fokker–Planck equation. Numerical tests one two dimensions drift–diffusion show converges exponentially constant non-constant advection diffusion velocities.
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ژورنال
عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering
سال: 2021
ISSN: ['0045-7825', '1879-2138']
DOI: https://doi.org/10.1016/j.cma.2021.114001