Convection enhanced diffusion for periodic flow
SIAM Journal on Applied Mathematics
Scalar transport in compressible flow
Physica D
Explicit volume-preserving and symplectic integrators for trigonometric polynomial flows
Journal of Computational Physics
Long-Run Accuracy of Variational Integrators in the Stochastic Context
SIAM Journal on Numerical Analysis
On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
SIAM Journal on Scientific Computing
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In this paper we study the problem of the numerical calculation (by Monte Carlo methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity field, in the limit of vanishing molecular diffusion. In this limit traditional numerical methods typically fail, since they do not represent accurately the geometry of the underlying deterministic dynamics. We propose a stochastic splitting method that takes into account the volume-preserving property of the equations of motion in the absence of noise, and when inertial effects can be neglected. An extension of the method is then proposed for the cases where the noise has a non-trivial time-correlation structure and when inertial effects cannot be neglected. The method of modified equations is used to explain failings of Euler-based methods. The new stochastic geometric integrators are shown to outperform standard Euler-based integrators. Various asymptotic limits of physical interest are investigated by means of numerical experiments, using the new integrators.