基于SPH方法与能量最小化算法平衡态模拟分析  

Equilibrium modeling and analysis based on SPH method and energy minimization algorithm

作　　者：梁广兵 罗贤兵 孙树瑜 LIANG Guangbing;LUO Xianbing;SUN Shuyu(School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China;Computational Transport Phenomena Laboratory, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia)

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025 [2]阿卜杜拉国王科技大学计算传递现象实验室,沙特阿拉伯图瓦23955-6900

出　　处：《合肥工业大学学报（自然科学版）》2022年第5期713-720,共8页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(51874262)。

摘　　要：文章基于双阱势(double-well potential,DWP)函数构造流体动力学中的能量泛函,形成一个能量最优化模型。利用光滑粒子流体动力学(smooth particle hydrodynamics,SPH)方法对模型进行格式离散,以梯度下降法进行求解,然后对系统能量的平衡态问题进行讨论和研究。以2个算例对模型进行数值验证,模拟结果表明,该模型可以很好地体现光滑粒子动力学方法和梯度下降法的有效性和准确性,为基于范德瓦尔斯方程或彭-罗宾逊方程的相平衡问题的研究奠定基础。An energy optimization model is proposed by constructing the energy functional in hydrodynamics based on the double-well potential(DWP)function.The model is discretized by using the smooth particle hydrodynamics(SPH)method and solved by gradient descent method.Therefore,the minimization of system energy and the equilibrium problem can be studied through this model.Finally,the model is verified by two examples,and the simulation results show the validity and accuracy of the SPH and gradient descent method,which lays a foundation for the research on the phase equilibrium problem of van der Waals fluid or Peng-Robinson fluid.

关 键 词：光滑粒子流体动力学(SPH) 能量 平衡态 双阱势(DWP) 梯度下降法 

分 类 号：O242.1[理学—计算数学]