Efficient numerical methods to solve the viscous-plastic sea ice model at high spatial resolutions
In this thesis, we develop efficient numerical methods to solve the viscous-plastic sea ice model on high resolution grids, with a cell size up to 2 km. This model describes the dynamical and thermodynamical large-scale processes in sea ice and plays an important role in climate models. The sea ice...
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| Format: | Doctoral or Postdoctoral Thesis |
| Language: | English |
| Published: |
2019
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| Online Access: | https://opendata.uni-halle.de//handle/1981185920/14142 https://doi.org/10.25673/14011 https://nbn-resolving.org/urn:nbn:de:gbv:ma9:1-1981185920-141421 |
| Summary: | In this thesis, we develop efficient numerical methods to solve the viscous-plastic sea ice model on high resolution grids, with a cell size up to 2 km. This model describes the dynamical and thermodynamical large-scale processes in sea ice and plays an important role in climate models. The sea ice component in climate models accounts for more than 20% of the overall computational effort. Thus, the development of efficient numerical methods is topic of current research. Sea ice dynamics are modeled by a system of equations coupling a nonlinear momentum equation, and transport processes. Currently, existing methods are based on implicit discretizations of the nonlinear momentum equation and converge either poorly or not at all on high resolution grids. Within a finite element framework, we present a new efficient Newton solver, globalized with a line search method and accelerated, with respect to convergence, by the operator-related damped Jacobian method. Using this novel approach we significantly improve the robustness of currently applied Newton solvers. We proove that the Jacobian of the sea ice model is positive definite, which provides global convergence of the Newton scheme, assuming an optimal damping parameter. As the used linear solver in the Jacobian-free Newton-Krylov approach is extremely costly, mainly due to the absence of efficient preconditioners, we introduce the geometric multigrid method as preconditioner to the linear solver. Analyzing an idealized test case on a 2 km grid, we find that the multigrid preconditioner is able to reduce the iteration count of the linear solver by up to 80% compared to an incomplete lower upper factorization as preconditioner. As the convergence rate of the multigrid method is robust with increasing mesh resolutions, it is a suitable method for sea ice simulations at high spatial resolutions. In the final part of the thesis, we develop a goal oriented error estimator for partitioned solution approaches, which is applicable to the sea ice model. The error estimator ... |
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