On formulations of compressible mantle convection
On formulations of compressible mantle convection
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可压缩地幔对流的公式
DOI：
10.1093/gji/ggaa078
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发表时间：
2020
影响因子：
2.8
通讯作者：
Myhill, Robert
中科院分区：
文献类型：
--
作者：
Gassmöller, Rene;Dannberg, Juliane;Bangerth, Wolfgang;Heister, Timo;Myhill, Robert
地球和其他行星上的地幔对流和长期岩石圈动力学可以看作是一种高粘性流体的缓慢变形，因此可以用可压缩的纳维-斯托克斯方程来描述。由于在地球大小的行星上，可压缩性的影响不是主要影响，与参考剖面的密度偏差最多只有几个百分点，并且使用完整的控制方程会带来数值上的挑战，因此大多数建模研究都简化了控制方程。常见的近似假设一个时间常数，但深度依赖于密度的参考剖面（非弹性液体近似），或者完全使用恒定的参考密度（Boussinesq近似）。在大多数以前的地幔对流和地壳动力学研究中，人们可以假设这些近似引入的误差与由于材料行为约束不佳和数值精度有限而导致的误差相比是很小的。然而，随着模型参数化变得更加现实，以及模型分辨率的提高，情况可能不再如此，使用简化的守恒方程所产生的误差可能不再可以忽略不计：虽然这种近似对于地幔柱或穿越整个地幔的板的模型可能是合理的，但对于经历相变的层状材料或经历显著加热或冷却的材料可能不令人满意。例如，在边界层或靠近动态变化的密度梯度处，使用上述可压缩性近似产生的误差可能是主要的误差来源，而常见的近似可能无法捕获感兴趣的物理行为。在本文中，我们讨论了连续性方程的新公式，其中包括由于温度，压力和成分而引起的动态密度变化，而不使用密度的参考剖面。我们量化了相对于许多基准模型中现有公式的精度改进，并评估了这些效果对哪些实际应用是重要的。最后，我们考虑新公式的数值方面。我们在免费提供的社区软件方面实现和测试这些公式，并将此代码用于我们的数值实验。
Mantle convection and long-term lithosphere dynamics in the Earth and other planets can be treated as the slow deformation of a highly viscous fluid, and as such can be described using the compressible Navier–Stokes equations. Since on Earth-sized planets the influence of compressibility is not a dominant effect, density deviations from a reference profile are at most on the order of a few percent and using the full governing equations poses numerical challenges, most modelling studies have simplified the governing equations. Common approximations assume a temporally constant, but depth-dependent reference profile for the density (the anelastic liquid approximation), or drop compressibility altogether and use a constant reference density (the Boussinesq approximation). In most previous studies of mantle convection and crustal dynamics, one can assume that the error introduced by these approximations was small compared to the errors that resulted from poorly constrained material behaviour and limited numerical accuracy. However, as model parametrizations have become more realistic, and model resolution has improved, this may no longer be the case and the error due to using simplified conservation equations might no longer be negligible: while such approximations may be reasonable for models of mantle plumes or slabs traversing the whole mantle, they may be unsatisfactory for layered materials experiencing phase transitions or materials undergoing significant heating or cooling. For example, at boundary layers or close to dynamically changing density gradients, the error arising from the use of the aforementioned compressibility approximations can be the dominant error source, and common approximations may fail to capture the physical behaviour of interest. In this paper, we discuss new formulations of the continuity equation that include dynamic density variations due to temperature, pressure and composition without using a reference profile for the density. We quantify the improvement in accuracy relative to existing formulations in a number of benchmark models and evaluate for which practical applications these effects are important. Finally, we consider numerical aspects of the new formulations. We implement and test these formulations in the freely available community softwareaspect, and use this code for our numerical experiments.
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影响因子：
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作者：
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通讯作者：
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期刊：
影响因子：
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影响因子：
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作者：
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