论文标题
改进的多组分流中熔化和溶解的相位场模型
Improved phase-field models of melting and dissolution in multi-component flows
论文作者
论文摘要
我们开发和分析了第一个二阶相位模型，以将熔融和溶解在多组分流中结合在一起。这提供了一种简单而准确的方法，可以模拟现有代码中的具有挑战性的相变问题。相位模型通过使用平滑相位场来描述单独区域来简化计算。相位场消除了追踪移动相边界的复杂离散的需求。但是，标准相位模型仅是一阶准确的。它们通常会导致与弥散界面厚度成正比的误差。我们通过开发一个通用框架来消除这种主导误差，用于对任意几何形状中的分散地下方法的渐近分析。使用此框架，我们可以始终统一以前的熔融和溶解的二阶相位模型以及用于流体固定相互作用的体积 - 五体方法。我们最终使用开源频谱代码Dedalus在两个综合基准问题中验证了模型的二阶收敛。
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.
