在有限元代码中实现体积-流体方法及其在地球地幔密度分层流体中热化学对流中的应用
Implementation of a Volume-of-Fluid Method in a Finite Element Code with Applications to Thermochemical Convection in a Density Stratified Fluid in the Earth's Mantle
AI总结：
本文描述了在开放源代码有限元代码ASPECT中实现第二阶精度的体积-流体界面追踪算法，用于模拟地幔中的热化学对流，展示了该方法的准确性和适应性网格细化的应用。
摘要：
我们描述了在开放源代码有限元代码ASPECT中实现第二阶精度的体积-流体界面追踪算法，该代码旨在模拟地幔中的对流。这包括求解不可压缩斯托克斯方程，与温度的输运扩散方程耦合，以及基于温度变化的密度依赖性所支配的布西尼耶公式，以及一个标记方程，用于指示两种初始密度状态。体积-流体方法完全并行化，并与ASPECT中的自适应网格细化算法集成。我们展示了几个标准界面追踪基准的结果，以证明该方法的准确性，以及计算地幔对流社区中常用的几个基准结果。最后，我们展示了具有和没有自适应网格细化的计算结果，用于计算一个热化学对流模型，该模型涉及计算上分层的流体，旨在提供关于热柱如何在地球表面形成洋中脊基岩的起源的见解，这些热柱最终到达地球表面作为洋中脊基岩，起源于被称为大低剪切波速度省的地球内核-地幔边界结构。
英文摘要：
We describe the implementation of a second-order accurate volume-of-fluid interface tracking algorithm in the open source finite element code ASPECT, which is designed to model convection in the Earth's mantle. This involves the solution of the incompressible Stokes equations coupled to an advection diffusion equation for the temperature, a Boussinesq approximation that governs the dependence of the density on the temperature, and an advection equation for a marker indicating the two initial density states. The volume-of-fluid method is fully parallelized and is integrated with the adaptive mesh refinement algorithm in ASPECT. We present the results of several standard interface tracking benchmarks in order to demonstrate the accuracy of the method as well as the results of several benchmarks commonly used in the computational mantle convection community. Finally, we present the results of computations with and without adaptive mesh refinement of a model problem involving thermochemical convection in a computationally stratified fluid designed to provide insight into how thermal plumes, that eventually reach the Earth's surface as ocean island basalts, originate at structures on the core-mantle boundary known as Large Low Shear wave Velocity Provinces.
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