A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows
<|reference_start|>A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows: This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between spatial and temporal variables for cases with anomalous diffusion phenomena. From a Lagrangian approach, we separate the corresponding stochastic differential equations (SDEs) into sub-problems and construct a one-step structure-preserving method to solve them. Then by modified equation systems, the convergence analysis in calculating the effective diffusivity is provided and compared between the structure-preserving scheme and the Euler-Maruyama scheme. Also, we provide the error estimate for the structure-preserving scheme in calculating the power law for a series of super-diffusive random flows. Finally, we calculate the effective diffusivity and anomalous diffusion phenomena for a series of 2D and 3D random fields.<|reference_end|>
@article{zhang2024a,
    title={A structure-preserving scheme for computing effective diffusivity and
  anomalous diffusion phenomena of random flows},
    author={Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang},
    journal={arXiv preprint arXiv:2405.19003},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.19003},
    primaryClass={math.NA cs.NA}
}