论文标题
完全隐式，准确地处理两相不可压缩的Navier-Stokes方程的跳跃条件
Fully implicit and accurate treatment of jump conditions for two-phase incompressible Navier-Stokes equation
论文作者
论文摘要
我们提出了一种用于两相不可压缩的Navier-Stokes方程的数值方法，在应力张量和材料属性中的正常分量中具有跳跃不连续性。尽管所提出的方法仅是一阶准确的，但它确实迅速捕获了不连续性，不会忽略或省略跳跃条件的任何组成部分。速度梯度和压力的不连续性使用奇异力和速度的切向衍生物的线性组合表达，以完全隐式的方式处理跳跃条件。应力张量发散的线性系统是在幽灵流体法的框架中构建的，并且通过迭代过程求解了所得的鞍点系统。数值结果支持这样的推断，即即使速度和压力在整个接口上不光滑，并且可以处理可能出现在现实世界中的模拟中，即使速度和压力不光滑，也可以在$ l^\ infty $规范中收敛。
We present a numerical method for two-phase incompressible Navier-Stokes equation with jump discontinuity in the normal component of the stress tensor and in the material properties. Although the proposed method is only first-order accurate, it does capture discontinuity sharply, not neglecting nor omitting any component of the jump condition. Discontinuities in velocity gradient and pressure are expressed using a linear combination of singular force and tangential derivatives of velocities to handle jump conditions in a fully implicit manner. The linear system for the divergence of the stress tensor is constructed in the framework of the ghost fluid method, and the resulting saddle-point system is solved via an iterative procedure. Numerical results support the inference that the proposed method converges in $L^\infty$ norms even when velocities and pressures are not smooth across the interface and can handle a large density ratio that is likely to appear in a real-world simulation.
