一种基于黎曼解处理大密度比多相流SPH的改进算法

多相流界面存在密度、黏性等物理场间断,直接采用传统光滑粒子水动力学(smoothedparticle hydrodynamics,SPH)方法进行数值模拟,界面附近的压力和速度存在震荡.一套基于黎曼解能够处理大密度比的多相流SPH计算模型被提出,该模型利用黎曼解在处理接触间断问题方面的优势,将黎曼解引入到SPH多相流计算模型中,为了能够准确求解多相流体物理黏性、减小黎曼耗散,对黎曼形式的SPH动量方程进行了改进,又将Adami固壁边界与黎曼单侧问题相结合来施加多相流SPH固壁边界,同时模型中考虑了表面张力对小尺度异相界面的影响,该模型没有添加任何人工黏性、人工耗散和非物理人工处理技术,能够反应多相流真实物理黏性和物理演变状态.采用该模型首先对三种不同粒子间距离散下方形液滴震荡问题进行了数值模拟,验证了该模型在处理异相界面的正确性和模型本身的收敛性;后又通过对Rayleigh--Taylor不稳定、单气泡上浮、双气泡上浮问题进行了模拟计算,结果与文献对比吻合度高,异相界面捕捉清晰,结果表明,本文改进的多相流SPH模型能够稳定、有效的模拟大密度比和黏性比的多相流问题. 

AN IMPROVED SPH ALGORITHM FOR LARGE DENSITY RATIOS MULTIPHASE FLOWS BASED ON RIEMANN SOLUTION1)

The discontinuities of physical fields (such as density, viscosity and so on) exist in the different phase interface of multiphase flow problems, and the numerical simulation method using the traditional SPH model is liable to cause spurious~oscillations in the pressure and velocity field at the interface, which is a big problem in the application of multiphase flows. An improved SPH model based on Riemann solution on dealing with the abrupt physical quantities of multiphase flows with large density radios is presented. Using the advantage of Riemann solution in dealing with the contact discontinuity problems, we introduce it into the SPH multiphase flow model. For the sake of accurately calculating the physical viscosity of multiphase fluid and decreasing the Riemann dissipation, the SPH momentum equation of the Riemann solution form is improved. In the new model, we combine the Adami fixed particle wall-boundary with the one-sided Riemann problem to impose solid boundary of the SPH multiphase flow, and consider the influence of the surface tension on the small-scale interface. The new model without adding any artificial viscosity, artificial dissipation and non-physical treatment technology can simulate the real physical viscousity and the physical evolution process of multiphase flow problems. In order to verify the ability of the improved model in dealing with the multiphase flow problems with the discontinuous interface and the convergence of the model particle spacing, firstly the squared droplet oscillating problem is simulated under different discrete particle spacing. Afterwards, the multiphase flow problems of the Rayleigh-Taylor instability, the single bubble buoyancy and the double bubble buoyancy are simulated. The interface is clearly capture and the results are good in agreement with the literature, which proved that the improved multiphase flow SPH model can stably and effectively deal with the problems of the multiphase flow large with density ratio and large viscosity ratio.