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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.15230 |
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| _version_ | 1866914164221411328 |
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| author | Huang, Can Wang, Weiwen Xu, Chuanju |
| author_facet | Huang, Can Wang, Weiwen Xu, Chuanju |
| contents | This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach, the scheme is fully explicit yet unconditionally stable. At each time step, it only requires solving Poisson-type equations with constant coefficients. To the best of our knowledge, this is the first application of the auxiliary variable method to stochastic Navier-Stokes equations. We provide a detailed strong convergence analysis for the linearized equation under standard assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise Huang, Can Wang, Weiwen Xu, Chuanju Numerical Analysis 60H15, 76D05, 65N12, 41A25 This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach, the scheme is fully explicit yet unconditionally stable. At each time step, it only requires solving Poisson-type equations with constant coefficients. To the best of our knowledge, this is the first application of the auxiliary variable method to stochastic Navier-Stokes equations. We provide a detailed strong convergence analysis for the linearized equation under standard assumptions. |
| title | An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise |
| topic | Numerical Analysis 60H15, 76D05, 65N12, 41A25 |
| url | https://arxiv.org/abs/2511.15230 |