稀薄气体区域内移动液滴的模拟
Simulation of a moving liquid droplet inside a rarefied gas region
AI总结：
本文通过耦合玻尔兹曼方程和不可压缩Navier-Stokes方程，采用有限点集法（FPM）和DSMC粒子方法，模拟了稀薄气体中移动液滴的动力学行为，并在连续介质区验证了耦合解与Navier-Stokes解的一致性。
摘要：
我们研究了在克努森数大范围内气体中液滴的动力学。移动液滴由不可压缩Navier-Stokes方程建模，周围稀薄气体由玻尔兹曼方程建模。推导了气液两相之间的界面边界条件。不可压缩Navier-Stokes方程采用一种称为有限点集法（FPM）的无网格拉格朗日粒子方法求解，玻尔兹曼方程采用DSMC类型的粒子方法求解。为了验证玻尔兹曼方程和不可压缩Navier-Stokes方程的耦合解，我们进一步在气相和液相中分别求解了可压缩和不可压缩Navier-Stokes方程。在后一种情况下，可压缩和不可压缩Navier-Stokes方程也由FPM求解。在连续介质区，由玻尔兹曼方程和不可压缩Navier-Stokes方程得到的耦合解与由可压缩和不可压缩Navier-Stokes方程得到的解相匹配。在本文中，我们展示了一维物理空间中的解。
英文摘要：
We study the dynamics of a liquid droplet inside a gas over a large range of the Knudsen numbers. The moving liquid droplet is modeled by the incompressible Navier-Stokes equations, the surrounding rarefied gas by the Boltzmann equation. The interface boundary conditions between the gas and liquid phases are derived. The incompressible Navier-Stokes equations are solved by a meshfree Lagrangian particle method called Finite Pointset Method (FPM), and the Boltzmann equation by a DSMC type of particle method. To validiate the coupled solutions of the Boltzmann and the incompressible Navier-Stokes equations we have further solved the compressible and the incompressible Navier-Stokes equations in the gas and liquid phases, respectively. In the latter case both the compressible and the incompressible Navier-Stokes equations are also solved by the FPM. In the continuum regime the coupled solutions obtained from the Boltzmann and the incompressible Navier-Stokes equations match with the solutions obtained from the compressible and the incompressible Navier-Stokes equations. In this paper, we presented solutions in one-dimensional physical space.
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