Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1137/19M1277163
- Scopus: eid_2-s2.0-85096595351
- WOS: WOS:000584721000025
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Convergence Analysis of Stochastic Structure-Preserving Schemes for Computing Effective Diffusivity in Random Flows
Title | Convergence Analysis of Stochastic Structure-Preserving Schemes for Computing Effective Diffusivity in Random Flows |
---|---|
Authors | |
Issue Date | 2020 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at https://www.siam.org/Publications/Journals/SIAM-Journal-on-Numerical-Analysis-SINUM |
Citation | SIAM Journal on Numerical Analysis, 2020, v. 58 n. 5, p. 3040-3067 How to Cite? |
Abstract | In this paper, we develop efficient stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of a passive tracer particle in random flows using the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). Then we propose stochastic structure-preserving schemes to solve the SDEs and provide rigorous convergence analysis for the numerical schemes in computing effective diffusivity. The convergence analysis follows a probabilistic approach, which interprets the solution process generated by our numerical schemes as a Markov process. By exploring the ergodicity of the solution process, we obtain a convergence analysis of our method in computing long-time solutions of the SDEs. Most importantly, our analysis result reveals the equivalence of the definition of the effective diffusivity by solving discrete-type and continuous-type (i.e., Eulerian) corrector problems, which is fundamental and interesting. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed method and investigate the convection-enhanced diffusion phenomenon in two- and three-dimensional incompressible random flows. |
Persistent Identifier | http://hdl.handle.net/10722/289266 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 2.163 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | LYU, J | - |
dc.contributor.author | WANG, Z | - |
dc.contributor.author | Xin, J | - |
dc.contributor.author | Zhang, Z | - |
dc.date.accessioned | 2020-10-22T08:10:13Z | - |
dc.date.available | 2020-10-22T08:10:13Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | SIAM Journal on Numerical Analysis, 2020, v. 58 n. 5, p. 3040-3067 | - |
dc.identifier.issn | 0036-1429 | - |
dc.identifier.uri | http://hdl.handle.net/10722/289266 | - |
dc.description.abstract | In this paper, we develop efficient stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of a passive tracer particle in random flows using the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). Then we propose stochastic structure-preserving schemes to solve the SDEs and provide rigorous convergence analysis for the numerical schemes in computing effective diffusivity. The convergence analysis follows a probabilistic approach, which interprets the solution process generated by our numerical schemes as a Markov process. By exploring the ergodicity of the solution process, we obtain a convergence analysis of our method in computing long-time solutions of the SDEs. Most importantly, our analysis result reveals the equivalence of the definition of the effective diffusivity by solving discrete-type and continuous-type (i.e., Eulerian) corrector problems, which is fundamental and interesting. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed method and investigate the convection-enhanced diffusion phenomenon in two- and three-dimensional incompressible random flows. | - |
dc.language | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at https://www.siam.org/Publications/Journals/SIAM-Journal-on-Numerical-Analysis-SINUM | - |
dc.relation.ispartof | SIAM Journal on Numerical Analysis | - |
dc.rights | © [2020] Society for Industrial and Applied Mathematics. First Published in [Publication] in [volume 48 number 5], published by the Society for Industrial and Applied Mathematics (SIAM). | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | Convergence Analysis of Stochastic Structure-Preserving Schemes for Computing Effective Diffusivity in Random Flows | - |
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 | 10.1137/19M1277163 | - |
dc.identifier.scopus | eid_2-s2.0-85096595351 | - |
dc.identifier.hkuros | 316274 | - |
dc.identifier.volume | 58 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 3040 | - |
dc.identifier.epage | 3067 | - |
dc.identifier.isi | WOS:000584721000025 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0036-1429 | - |