We present a novel numerical method to solve the incompressible Navier-Stokes equations for two-phase flows with phase change. Separate phases are tracked using a geometric Volume-Of-Fluid (VOF) method with piecewise linear interface construction (PLIC). Thermal energy advection is treated in conservative form and the geometric calculation of VOF fluxes at computational cell boundaries is used consistently to calculate the fluxes of heat capacity. The phase boundary is treated as sharp (infinitely thin), which leads to a discontinuity in the velocity field across the interface in the presence of phase change. The numerical difficulty of this jump is accommodated with the introduction of a novel two-step VOF advection scheme. The method has been implemented in the open source code PARIS and is validated using well-known test cases. These include an evaporating circular droplet in microgravity (2D), the Stefan problem and a 3D bubble in superheated liquid. The accuracy shown in the results were encouraging. The 2D evaporating droplet showed excellent prediction of the droplet volume evolution as well as preservation of its circular shape. A relative error of less than 1% was achieved for the Stefan problem case, using water properties at atmospheric conditions. Two cases of a bubble in superheated liquid was performed, at respective Jacob numbers of 0.5 and 2.15. For the final radius of the bubbles in both cases, a relative error of less than 7% was obtained on the coarsest grid, with less than 1% on the finest.

我们提出了一种新的数值方法来求解带相变的两相流不可压缩的Navier-Stokes方程。使用具有分段线性界面构造（PLIC）的几何体积（VOF）方法跟踪单独的相。热能对流以保守的形式处理，VOF通量在计算单元边界处的几何计算始终用于计算热容通量。相界被视为尖锐（无限薄），这会导致在存在相变时跨界面的速度场不连续。引入新颖的两步式VOF平流方案可解决这种跳跃的数值难度。该方法已在开源代码PARIS中实现并使用众所周知的测试用例进行了验证。这些包括微重力（2D）中蒸发的圆形液滴，斯特凡问题以及过热液体中的3D气泡。结果显示的准确性令人鼓舞。二维蒸发液滴显示出对液滴体积演变以及保持其圆形形状的出色预测。使用大气条件下的水属性，对于Stefan问题而言，相对误差小于1％。发生了两种情况的过热液体中的气泡，分别的雅各布数为0.5和2.15。在这两种情况下，对于气泡的最终半径，在最粗糙的网格上获得的相对误差均小于7％，而在最细网格上的相对误差则小于1％。