基于弱可压与不可压光滑粒子动力学方法的封闭方腔自然对流数值模拟及算法对比

为了对比研究弱可压光滑粒子动力学(WCSPH)方法和不可压光滑粒子动 力学(ISPH)方法在模拟封闭方腔自然对流问题时的特性, 采用粒子位移技术有效地解决了高瑞利数条件下, 拉格朗日型SPH方法模拟封闭方腔自然对流时流体域内的粒子聚集和空穴问题, 将拉格朗日型SPH 方法求解封闭方腔自然对流问题的最高瑞利数提高到了10⁶; 进而通过对比瑞利数分别为10⁴, 10⁵, 10⁶的条件下, 采用拉格朗日型WCSPH、 拉格朗日型ISPH、欧拉型ISPH三种SPH方法模拟得到的封闭方腔速度分布云图、 温度分布云图、壁面努赛尔特数分布曲线和平均努塞尔特数, 分析了三种SPH方法在模拟封闭方腔自然对流时的精度、稳定性和计算效率. 结果表明: 在低瑞利数条件下, 以上三种SPH方法都可以较好地模拟此问题, 在高瑞利数条件下, 欧拉型ISPH方法的模拟结果最为精确; 拉格朗日型WCSPH方法模拟所得结果比拉格朗日型ISPH方法模拟所得结果稍好些. 关键词： 光滑粒子动力学 不可压光滑粒子动力学 粒子位移技术 自然对流

Comparisons among weakly-compressible and incompressible smo othed particle hdro dynamic algorithms for natural convection

Smoothed particle hydrodynamic (SPH) method is used to solve a variety of complex engineering problems. In the literature about SPH, there are two approaches to solving the pressure component of momentum conservation equation, namely incompressible SPH (ISPH) and weakly compressible SPH (WCSPH) methods. In this paper, we present a new comparative study of WCSPH (Lagrange), ISPH (Lagrange) and ISPH (Euler) methods, focusing on heat conduction issue by numerical solutions of natural convection in a square cavity. Temperature distributions, velocity distributions and Nusselt number distributions at different Rayleigh numbers (Ra=10⁴, 10⁵, 10⁶) are provided in the paper. The quantitative comparisons of results show that WCSPH (Lagrange), ISPH (Lagrange) and ISPH (Euler) methods all perform very well at low Rayleigh number. And at high Rayleigh number, SPH (Lagrange) needs shifting particle technology to correct the distribution of particles, ISPH (Euler) performs best because of the motionless particles, WCSPH (Lagrange) performs better than ISPH (Lagrange).
Keywords： smoothed particle hydrodynamics incompressible smoothed particle hydrodynamics shifting particle technology natural convection