An implicit free surface algorithm for geodynamical simulations

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• 作者：Stephan C. Kramer^a ; ^b ; ^{s.kramer@imperial.ac.uk} ; Cian R. Wilson^c ; D. Rhodri Davies^a
• 关键词：Free surface ; Topography ; Dynamics of lithosphere and mantle ; Tectonics and landscape evolution ; Numerical methods and analysis
• 刊名：Physics of the Earth and Planetary Interiors
• 出版年：2012
• 期刊代码：73_00319201
• 类别：ear
• 出版时间：March, 2012
• 卷：194-195
• 期：Complete
• 页码：25-37
• 文件大小：1103 K

摘要

Identifying the dominant controls on Earth鈥檚 surface topography is of critical importance to understanding both the short- and long-term evolution of geological processes and past- and present-day dynamics of Earth鈥檚 coupled mantle-lithosphere system. The ability to simulate a stress free 鈥?or a so-called 鈥榝ree surface鈥?鈥?boundary condition is required to examine such processes via numerical models. However, at present, geodynamical models incorporating a free surface are limited, as most underlying free surface algorithms place severe restrictions on the computational timestep. Consequently, the simulations are often intractable. In this study, we introduce a new approach for incorporating a free surface within geodynamical models: an algorithm, in which free surface elevation is treated as an independent variable and is solved for in conjunction with the momentum and continuity equation, using implicit time integration. We demonstrate that the method is straightforward to implement in existing models and, using a series of analytical and benchmark comparisons, we show that it does not suffer from the timestep constraints of previous schemes. Furthermore, the scheme can be made second order accurate in time, at no additional cost. The method therefore dramatically improves the computational efficiency of geodynamical simulations including a free surface, whilst maintaining solution accuracy.