应用FPM方法模拟封闭方腔自然对流

为验证有限粒子方法（FPM）能否很好地模拟自然对流问题，采用FPM方法对封闭方腔自然对流问题进行了数值模拟. 对FPM方法进行详细描述，并利用FPM方法对拉格朗日型的N-S方程进行离散，基于离散后的方程对瑞利数Ra分别为104，105，106的封闭方腔自然对流问题进行数值模拟，给出了不同瑞利数条件下的速度和温度云图以及中心线上量纲一的速度和温度分布曲线. 结果表明，FPM方法能够获得较准确的温度分布规律，当瑞利数较低时也能获得较准确的速度分布规律，但随着瑞利数的增大，速度场的模拟结果精度和稳定性变差，因此为了获得更准确和光滑的速度分布场，需要对FPM方法做进一步的改进. 

Finite Particle Method (FPM) Modeling of Natural Convection in a Closed Square Cavity

In order to test the ability of FPM modelling natural convection problems, FPM was used to simulate natural convection in a closed square cavity. Firstly,FPM was depicted in detail, the Lagrangian N-S equations was discretized with FPM, and natural convection in a closed square was simulated at Ra=10⁴,10⁵,10⁶ based on the discretized equations. And then, velocity and temperature contours, non-dimensional velocity and temperature profiles along the centerline at different Rayleigh numbers were presented. The results show that FPM can obtain temperature field accurately at all three Rayleigh numbers and obtain velocity field accurately at low Raleigh numbers, but with increasing Raleigh numbers, the precision and stability of the velocity field is decreasing, so FPM still needs to be improved for getting more accurate and stable velocity fields.