Name
Title | ||
|---|---|---|
Convergence Analysis of Stochastic Structure-Preserving Schemes for Computing Effective Diffusivity in Random Flows. |
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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/19M1277163 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | DocType | Volume |
convection-enhanced diffusion,random flows,structure-preserving schemes,corrector problem,ergodic theory,Markov process | Journal | 58 |
Issue | ISSN | Citations |
5 | 0036-1429 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Junlong Lyu | 1 | 0 | 1.01 |
| Zhongjian Wang | 2 | 3 | 2.43 |
| Jack Xin | 3 | 212 | 25.49 |
| Zhiwen Zhang | 4 | 0 | 0.34 |