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Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes. (English) Zbl 1404.65209

A passive tracer model, which describes particle motion with zero inertia, is studied. The effective diffusivity of chaotic and stochastic flows is computed using structure-preserving schemes. Instead of solving the Fokker-Planck equation in the Eulerian formulation, the motion of particles is computed in the Lagrangian formulation, modelled by stochastic differential equations. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several typical chaotic and stochastic flow problems of physical interest. Moreover, a rigorous error analysis is provided, and the existence of residual diffusivity is investigated for several prototype velocity fields.

MSC:

65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
35Q84 Fokker-Planck equations
35R60 PDEs with randomness, stochastic partial differential equations
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
76R99 Diffusion and convection
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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