A new formulation for coupled magma/mantle dynamics
A new formulation for coupled magma/mantle dynamics
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DOI：
10.1093/gji/ggz190
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发表时间：
2018-10
影响因子：
2.8
通讯作者：
J. Dannberg;Rene Gassmöller;Ryan R. Grove;T. Heister
中科院分区：
文献类型：
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作者：
J. Dannberg;Rene Gassmöller;Ryan R. Grove;T. Heister
地球科学中的许多悬而未决的问题只能通过模拟熔体通过粘性变形固体岩石基质的多孔流动来理解。然而，描述该过程的方程组在熔融分数为零的极限下在数学上退化。不考虑这种简并性或仅通过正则化特定材料性质来避免简并性的数值方法通常在熔体分数在域的某些部分接近零时就变得计算昂贵。在这里，我们提出了一个新的配方的耦合岩浆/地幔动力学方程，解决这个问题，并允许它准确地计算大规模的3-D岩浆/地幔动力学模拟与广泛的零熔融分数的区域。我们实现这一点，通过重新调整的解决方案的变量之一，压实压力，这确保了消失的熔体分数，导致退化的方程成为一个身份和其他两个方程恢复到斯托克斯系统。这使我们能够将域分为两部分，并解决耦合的岩浆/地幔动力学系统，只有在熔体存在的细胞。我们已经实现了这个配方的开源地球动力学建模代码ASPECT和说明改进的性能相比，以前的三个字段的配方，数值显示，新的配方是最佳的问题大小，只有最低限度的敏感模型参数。除此之外，我们展示了现实问题的适用性，显示大规模的2-D和3-D模型的洋中脊复杂的流变学。因此，我们相信，我们的新配方及其在ASPECT中的实施将证明是一个有价值的工具，用于研究熔体分离的相互作用，并与固体主岩石在地球和其他行星机构使用高分辨率，三维模拟。
Many open problems in the Earth sciences can only be understood by modelling the porous flow of melt through a viscously deforming solid rock matrix. However, the system of equations describing this process becomes mathematically degenerate in the limit of vanishing melt fraction. Numerical methods that do not consider this degeneracy or avoid it solely by regularising specific material properties generally become computationally expensive as soon as the melt fraction approaches zero in some part of the domain. Here, we present a new formulation of the equations for coupled magma/mantle dynamics that addresses this problem, and allows it to accurately compute large-scale 3-D magma/mantle dynamics simulations with extensive regions of zero melt fraction. We achieve this by rescaling one of the solution variables, the compaction pressure, which ensures that for vanishing melt fraction, the equation causing the degeneracy becomes an identity and the other two equations revert to the Stokes system. This allows us to split the domain into two parts, and to solve the coupled magma/mantle dynamics system only in cells where melt is present. We have implemented this formulation in the open source geodynamic modelling code ASPECT and illustrate the improved performance compared to the previous three-field formulation, showing numerically that the new formulation is optimal in terms of problem size and only minimally sensitive to model parameters. Beyond that, we demonstrate the applicability to realistic problems by showing large-scale 2-D and 3-D models of mid-ocean ridges with complex rheology. Hence, we believe that our new formulation and its implementation in ASPECT will prove a valuable tool for studying the interaction of melt segregating through and interacting with a solid host rock in the Earth and other planetary bodies using high-resolution, three-dimensional simulations.