It takes three to tango: 1. Simulating buoyancy‐driven flow in the presence of large viscosity contrasts
It takes three to tango: 1. Simulating buoyancy‐driven flow in the presence of large viscosity contrasts
复制标题
探戈需要三个步骤： 1. 在存在大粘度对比的情况下模拟浮力驱动的流动
DOI：
10.1029/2009jb006916
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发表时间：
2010
影响因子：
--
通讯作者：
B. Hager
中科院分区：
文献类型：
--
作者：
J. Suckale;Jean;B. Hager
[1]浮力驱动流对许多地球动力学现象具有根本的重要性。由于控制多相流的运动方程很少服从解析解，数值模拟提供了一个令人信服的替代方案。它们能够仔细分析不同状态、初始条件和流动动力学下的流动现象。这些计算中的三个关键挑战是（1）在存在大粘度对比的情况下运动方程的精确解，（2）不同流体之间的强烈变形界面的表示，以及（3）流体和界面求解器的精确耦合。在三维中，这些挑战变得更加复杂，并且数值方案的适当选择对计算模拟的易处理性，准确性，鲁棒性和效率具有深远的影响。这是第一个文件的两个，研究数值模拟浮力驱动的流动中存在的大粘度对比。在本文中，我们提出了我们的数值方法，解决了上述三个主要的挑战，通过结合三种数值方法，即（1）一个扩展的幽灵流体类型的离散化，我们专门开发的斯托克斯制度，（2）水平集方法，（3）扩展速度技术。我们发现，所有这三个组件是至关重要的，以获得一个通用的数值工具，模拟复杂的结构，不断变化的流动。我们通过在二维和三维中重现四个基准问题来验证我们的代码。我们特别注意比较我们的方法与其他现有的技术，详细介绍了这种方法的优点。最后，我们强调几种类型的地球物理流问题，我们相信我们的方法是非常适合的。
[1] Buoyancy-driven flow is of fundamental importance for numerous geodynamic phenomena. Since the equations of motion governing multiphase flow are rarely amenable to analytical solutions, numerical simulations provide a compelling alternative. They offer the ability to carefully analyze flow phenomena under differing regimes, initial conditions, and flow dynamics. The three key challenges in these computations are (1) the accurate solution of the equations of motion in the presence of large viscosity contrasts, (2) the representation of strongly deforming interfaces between different fluids, and (3) the accurate coupling of fluid and interface solver. In three dimensions, these challenges become even more intricate, and the appropriate choice of numerical scheme has a profound influence on the tractability, accuracy, robustness, and efficiency of the computational simulation. This is the first paper of two that examine numerical simulations of buoyancy-driven flow in the presence of large viscosity contrasts. In this paper, we present our numerical approach which tackles the above three main challenges through a combination of three numerical methods, namely, (1) an extended ghost fluid type discretization which we developed specifically for the Stokes regime, (2) the level set method, and (3) the extension velocity technique. We find that all three components are crucial to obtain a versatile numerical tool for simulating complex structures in evolving flow. We validate our code by reproducing four benchmark problems in two and three dimensions. We devote special attention to comparing our method to other existing techniques, detailing the advantages of this approach. Finally, we highlight several types of geophysical flow problems for which we believe our method to be well suited.