论文标题
一种尖锐的数值方法，用于模拟Stefan问题的对流效果
A Sharp Numerical Method for the Simulation of Stefan Problems with Convective Effects
论文作者
论文摘要
我们提出了一种数值方法，用于通过Stefan模型和不可压缩的流体流量控制的界面生长溶液。提出了一种算法，该算法要特别注意在温度，流速和压力以及界面速度上执行尖锐的界面条件。该方法利用级别的方法进行敏锐和隐式接口跟踪，自适应QuadTree网格上的混合有限差异/有限数量离散以及用于解决不可压缩Navier-Stokes方程的无压力投影方法。首先，使用合成解决方案对该方法进行数值收敛测试验证。然后，进行了横流圆柱上的冰形成的计算研究，并与现有的实验结果提供了良好的定量一致性，从而再现了过去实验中观察到的定性现象。最后，我们研究了不同的雷诺和斯特凡数在新兴界面形态上的作用，并在界面处局部和平均热传递的时间演变时提供了新的见解。
We present a numerical method for the solution of interfacial growth governed by the Stefan model coupled with incompressible fluid flow. An algorithm is presented which takes special care to enforce sharp interfacial conditions on the temperature, the flow velocity and pressure, and the interfacial velocity. The approach utilizes level-set methods for sharp and implicit interface tracking, hybrid finite-difference/finite-volume discretizations on adaptive quadtree grids, and a pressure-free projection method for the solution of the incompressible Navier-Stokes equations. The method is first verified with numerical convergence tests using a synthetic solution. Then, computational studies of ice formation on a cylinder in crossflow are performed and provide good quantitative agreement with existing experimental results, reproducing qualitative phenomena that have been observed in past experiments. Finally, we investigate the role of varying Reynolds and Stefan numbers on the emerging interface morphologies and provide new insights around the time evolution of local and average heat transfer at the interface.
