Abstract The extended finite element method (XFEM) and the level set method (LSM) are applied to simulate the solidification phenomenon and the behavior of the liquid-solid phase transition. The temperature-based energy equation is loosely-coupled with the incompressible Navier-Stokes (INS) equations and solved by XFEM using the Stefan condition to express the energy conservation law for phase change. The INS equations are additionally supplemented with the Boussinesq approximation for the buoyancy force that drives the ensuing melt flow. The temperature, pressure, and fluid velocity are discontinuous at the interface, and the LSM implicitly captures its location. A modified abs-enrichment scheme (where abs stands for the absolute value function) is used for the weakly-discontinuous temperature field, and a sign-enrichment scheme is employed for the strongly-discontinuous pressure field. The penalty method imposes the interface temperature and velocity and allows for fluid-structure interactions. The numerical model is verified with several benchmark tests: 1D solidification, infinite corner solidification, Frank sphere, flow over a cylinder, as well as tin melting with non-constant density. Once the simulation results have been shown to be in good agreement with analytical solutions and results obtained with other methods, the present methodology is applied to a melting ice cylinder at a high Reynolds number.

中文翻译：

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流固耦合：扩展 FEM 凝固方法

摘要 应用扩展有限元法（XFEM）和水平集法（LSM）模拟凝固现象和液固相变行为。基于温度的能量方程与不可压缩的纳维-斯托克斯 (INS) 方程松散耦合，并通过 XFEM 求解，使用 Stefan 条件表达相变的能量守恒定律。INS 方程还补充有用于驱动随后熔体流动的浮力的 Boussinesq 近似值。界面处的温度、压力和流体速度是不连续的，LSM 隐式地捕获了它的位置。修改后的 abs 富集方案（其中 abs 代表绝对值函数）用于弱不连续温度场，强不连续压力场采用符号富集方案。惩罚方法强加了界面温度和速度，并允许流固耦合。数值模型通过多项基准测试进行验证：一维凝固、无限角凝固、弗兰克球体、圆柱体流动以及非恒定密度的锡熔化。一旦模拟结果被证明与解析解和用其他方法获得的结果非常一致，本方法就被应用于高雷诺数的融化冰圆柱体。无限角凝固，弗兰克球体，流过圆柱体，以及非恒定密度的锡熔化。一旦模拟结果被证明与解析解和用其他方法获得的结果非常一致，本方法就被应用于高雷诺数的融化冰圆柱体。无限角凝固，弗兰克球体，流过圆柱体，以及非恒定密度的锡熔化。一旦模拟结果被证明与解析解和用其他方法获得的结果非常一致，本方法就被应用于高雷诺数的融化冰圆柱体。