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Article: Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes
Title | Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes |
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Authors | |
Keywords | Backward error analysis Chaotic Diffusion enhancement Effective diffusivity Stochastic flows |
Issue Date | 2018 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sinum.php |
Citation | SIAM Journal on Numerical Analysis, 2018, v. 56 n. 4, p. 2322-2344 How to Cite? |
Abstract | In this paper, we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition, we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual diffusion refers to the nonzero effective (homogenized) diffusion in the limit of zero molecular diffusion as a result of chaotic mixing of the streamlines. In this limit, traditional numerical methods typically fail since the solutions of the advection-diffusion equations develop sharp gradients. Instead of solving the Fokker–Planck equation in the Eulerian formulation, we compute the motion of particles in the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). We propose an effective numerical integrator based on a splitting method to solve the corresponding SDEs in which the deterministic subproblem is symplectic preserving while the random subproblem can be viewed as a perturbation. We provide rigorous error analysis for the new numerical integrator using the backward error analysis technique and show that our method outperforms standard Euler-based integrators. 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. The existence of residual diffusivity for these flow problems is also investigated. |
Persistent Identifier | http://hdl.handle.net/10722/260463 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 2.163 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Wang, Z | - |
dc.contributor.author | Xin, J | - |
dc.contributor.author | Zhang, Z | - |
dc.date.accessioned | 2018-09-14T08:42:10Z | - |
dc.date.available | 2018-09-14T08:42:10Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | SIAM Journal on Numerical Analysis, 2018, v. 56 n. 4, p. 2322-2344 | - |
dc.identifier.issn | 0036-1429 | - |
dc.identifier.uri | http://hdl.handle.net/10722/260463 | - |
dc.description.abstract | In this paper, we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition, we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual diffusion refers to the nonzero effective (homogenized) diffusion in the limit of zero molecular diffusion as a result of chaotic mixing of the streamlines. In this limit, traditional numerical methods typically fail since the solutions of the advection-diffusion equations develop sharp gradients. Instead of solving the Fokker–Planck equation in the Eulerian formulation, we compute the motion of particles in the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). We propose an effective numerical integrator based on a splitting method to solve the corresponding SDEs in which the deterministic subproblem is symplectic preserving while the random subproblem can be viewed as a perturbation. We provide rigorous error analysis for the new numerical integrator using the backward error analysis technique and show that our method outperforms standard Euler-based integrators. 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. The existence of residual diffusivity for these flow problems is also investigated. | - |
dc.language | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sinum.php | - |
dc.relation.ispartof | SIAM Journal on Numerical Analysis | - |
dc.rights | © 2018 Society for Industrial and Applied Mathematics. First Published in SIAM Journal on Numerical Analysis in volume 56, issue 4, published by the Society for Industrial and Applied Mathematics (SIAM). | - |
dc.subject | Backward error analysis | - |
dc.subject | Chaotic | - |
dc.subject | Diffusion enhancement | - |
dc.subject | Effective diffusivity | - |
dc.subject | Stochastic flows | - |
dc.title | Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes | - |
dc.type | Article | - |
dc.identifier.email | Zhang, Z: zhangzw@hku.hk | - |
dc.identifier.authority | Zhang, Z=rp02087 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1137/18M1165219 | - |
dc.identifier.scopus | eid_2-s2.0-85053542125 | - |
dc.identifier.hkuros | 291364 | - |
dc.identifier.volume | 56 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 2322 | - |
dc.identifier.epage | 2344 | - |
dc.identifier.isi | WOS:000443291900014 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0036-1429 | - |