热力学状态方程的几种数值求解方法

Numeric methods of solving EOS

给出了4种热力学状态方程求摩尔体积的求解算法,讨论了这些算法的数学原理、收敛特性和具体迭代格式,并以Peng-Robinson方程为例进行了具体计算和比较。主要结论:简单迭代法收敛稳定但收敛速度慢;Aitken-Steffensen方法简单、稳定且和Newton方法具有相同的二阶收敛;Newton方法速度较快但算法比较复杂,需要计算导数;加速Newton方法速度最快但最复杂。推荐优先使用Aitken-Steffensen方法,其次是加速Newton方法。

Four methods of solving molar volume from equation of state were proposed.The mathematic principle,convergence and iteration formats of these methods were studied.Taken Peng-Robinson equation as an example,molar volume was calculated using these methods.Main results show that simple iteration convergence is stable but slow,and Aitken-Steffensen iteration convergence is stable and quick and has the same convergence order as Newton iteration.Newton iteration convergence is quick but it needs the calculation of derivative.Accelerated Newton iteration convergence is most quick but calculation is most complex.Aitken-Steffensen method is recommended first and then the accelerated Newton method.