物理学报Issue(6)：1-6,6.DOI:10.7498/aps.64.064702
混合物状态方程的计算∗
Calculation of equation of state of a material mixture
摘要
Abstract
The problem of calculating the equation of state (EOS) of a material mixture often comes from fluid-dynamical system containing multiple materials. Generally, the EOS of a material mixture is a system of nonlinear equations which are usually solved by the tabular method and the Newton iterative method. However, the former has poor accuracy, and the later has a finite radius of convergence and hence will converge only if the initial guess is sufficiently close to the final solution. So, a procedure different from the above two method is presented for calculating the EOS of a material mixture whose constituents are in pressure equilibrium and temperature equilibrium. An imbedding method is used to determine the constituent partial thermodynamic variables subjected to the constraints that the total volume and energy of mixture and the constituent mass fractions are specified. The imbedding method has a large radius of convergence, introducing a parameter defined in the interval [0, 1] and a system of imbedding equations which is linearly composed of the to-be-solved EOS of a material mixture and the easy-to-solve EOS of a material mixture. While the parameter changes continuously from 0 to 1, the imbedding method continuously changes the solution of the to-be-solved EOS which the easy-to-solve EOS of a material mixture is continuously converted into. The system of imbedding equations can be changed into a system of ordinary differential form by taking the parameter as independent variable, easily solved by a matured computational method such as trapezoidal rule. By using thermodynamic formulae, two equations in the generalized Maxwellian form are obtained, relating respectively the pressure rate and temperature rate to the strain rate and the constituent mass fraction rate. Finally, the computational method is verified by calculating the EOS of various mass fractions of lead and tin mixture.关键词
混合物/状态方程/迭代法/Maxwell方程Key words
equation of state/material mixture/iteration algorithm/equation of Maxwellian form引用本文复制引用
周洪强,于明,孙海权,何安民,陈大伟,张凤国,王裴,邵建立..混合物状态方程的计算∗[J].物理学报,2015,(6):1-6,6.基金项目
中国工程物理研究院科学技术发展基金(批准号:2013A0201010)和国家自然科学基金(批准号:11272064)资助的课题.* Project supported by the Science and Technology Development Foundation of China Academy of Engineering Physics (Grant No.2013A0201010) and the National Natural Science Foundation of China (Grant No.11272064) （批准号:2013A0201010）
