多组分流动中熔化和溶解的改进相场模型
Improved phase-field models of melting and dissolution in multi-component flows
摘要：
我们开发和分析了第一个二阶相场模型，结合多组分流动中的熔化和溶解。这提供了一种简单而准确的方法来模拟现有代码中具有挑战性的相变问题。相场模型通过使用平滑的相场来描述分离的区域来简化计算。相场消除了跟踪移动相边界的复杂离散化的需要。然而，标准的相场模型只有一阶精度。它们经常引起与漫射界面的厚度成比例的误差。我们消除了这种主导性的错误，通过开发一个通用的框架，在任意几何形状的扩散界面方法的渐近分析。有了这个框架，我们可以一致地统一以前的二阶相场模型的熔化和溶解和流体-固体相互作用的体积罚方法。最后，我们使用开源谱代码Dedalus在两个全面的基准问题中验证了我们的模型的二阶收敛性。
英文摘要：
We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretisations that track the moving phase boundary. However standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.
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