Adaptively Implicit Advection for Atmospheric Flows
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arXiv
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| Format: | Preprint |
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2024
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| author | Weller, Hilary Kuehnlein, Christian Smolarkiewicz, Piotr K. |
| author_facet | Weller, Hilary Kuehnlein, Christian Smolarkiewicz, Piotr K. |
| contents | Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit advection scheme facilitates efficient and robust integrations with long time-steps while having negligible impact on the overall accuracy, and achieving monotonicity and local conservation on general meshes. A novel and important aspect for the efficiency of the approach is that only one linear solver iteration is needed for each advection solve.
The implementation in this paper uses a second-order Runge-Kutta implicit/explicit time-stepping in combination with a second/third-order finite volume spatial discretisation. We demonstrate the adaptively implicit advection in the context of deformational flow advection on the sphere and a fully compressible model for atmospheric flows. Tracers are advected over the poles of latitude-longitude grids with very large Courant numbers and through hexagonal and cubed-sphere meshes with the same algorithm. Buoyant flow simulations with strong local updrafts also benefit from adaptively implicit advection. Stably stratified flow simulations require a stable combination of implicit treatment of gravity and acoustic waves as well as advection in order to achieve long stable time-steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptively Implicit Advection for Atmospheric Flows Weller, Hilary Kuehnlein, Christian Smolarkiewicz, Piotr K. Fluid Dynamics Numerical Analysis Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit advection scheme facilitates efficient and robust integrations with long time-steps while having negligible impact on the overall accuracy, and achieving monotonicity and local conservation on general meshes. A novel and important aspect for the efficiency of the approach is that only one linear solver iteration is needed for each advection solve. The implementation in this paper uses a second-order Runge-Kutta implicit/explicit time-stepping in combination with a second/third-order finite volume spatial discretisation. We demonstrate the adaptively implicit advection in the context of deformational flow advection on the sphere and a fully compressible model for atmospheric flows. Tracers are advected over the poles of latitude-longitude grids with very large Courant numbers and through hexagonal and cubed-sphere meshes with the same algorithm. Buoyant flow simulations with strong local updrafts also benefit from adaptively implicit advection. Stably stratified flow simulations require a stable combination of implicit treatment of gravity and acoustic waves as well as advection in order to achieve long stable time-steps. |
| title | Adaptively Implicit Advection for Atmospheric Flows |
| topic | Fluid Dynamics Numerical Analysis |
| url | https://arxiv.org/abs/2406.08640 |