A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911892220411904 |
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| author | Zhang, Tan Wang, Zhongjian Xin, Jack Zhang, Zhiwen |
| author_facet | Zhang, Tan Wang, Zhongjian Xin, Jack Zhang, Zhiwen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows Zhang, Tan Wang, Zhongjian Xin, Jack Zhang, Zhiwen Numerical Analysis 37M25, 60J60, 60H35, 65P10, 65M75, 76M50 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. |
| title | A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows |
| topic | Numerical Analysis 37M25, 60J60, 60H35, 65P10, 65M75, 76M50 |
| url | https://arxiv.org/abs/2405.19003 |