薄带中有沉淀和溶解的Cahn-Hilliard Navier-Stokes模型的尺度放大
Upscaling of a Cahn-Hilliard Navier-Stokes Model with Precipitation and Dissolution in a Thin Strip
摘要：
本文考虑了两种不互溶流体不可压缩流动的相场模型。该模型通过包括第三固相来扩展两个流体相的广泛模型，第三固相可以由于例如沉淀和溶解而演变。我们考虑一个简单的，二维几何形状的薄带，它仍然可以被看作是一个单一的孔喉在多孔介质中的代表。在适当的假设下，对Peclet数和毛细管数，我们调查的极限情况下，当带的宽度和长度之间的比率将为零。以这种方式，并采用横向平均，我们得到一个放大模型。其结果是一个多尺度的模型，包括放大的总通量和离子传输的方程，而相场方程必须在细胞的问题，在孔隙尺度，以确定接口的位置来解决。我们还研究了多尺度模型的锐界面极限，在该极限下相场参数接近0。由此产生的尖锐界面模型只包括达西尺度方程，因为细胞的问题可以明确解决。值得注意的是，我们发现的渐近一致性，这是升尺度过程和尖锐的接口极限交换。我们使用数值结果调查的有效性时，不连续性形成的升尺度模型。
英文摘要：
We consider a phase-field model for the incompressible flow of two immiscible fluids. This model extends widespread models for two fluid phases by including a third, solid phase, which can evolve due to e.g. precipitation and dissolution. We consider a simple, two-dimensional geometry of a thin strip, which can still be seen as the representation of a single pore throat in a porous medium. Under moderate assumptions on the Peclet number and the capillary number, we investigate the limit case when the ratio between the width and the length of the strip is going to zero. In this way and employing transversal averaging, we derive an upscaled model. The result is a multi-scale model consisting of the upscaled equations for the total flux and the ion transport, while the phase-field equation has to be solved in cell-problems at the pore scale to determine the position of interfaces. We also investigate the sharp-interface limit of the multi-scale model, in which the phase-field parameter approaches 0. The resulting sharp-interface model consists only of Darcy-scale equations, as the cell-problems can be solved explicitly. Notably we find asymptotic consistency, that is the upscaling process and the sharp-interface limit commute. We use numerical results to investigate the validity of the upscaling when discontinuities are formed in the upscaled model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
