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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 6473234, 9 pages
Research Article

A Study on the Efficient Method for the Solution of the Saha Equation in the Numerical Simulation of Capillary Discharge

1School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
2State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Correspondence should be addressed to Cheng Wu; nc.ude.tib@uwgnehc

Received 14 June 2017; Revised 17 August 2017; Accepted 22 October 2017; Published 20 November 2017

Academic Editor: Prabir Daripa

Copyright © 2017 Hengzhu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the numerical simulation of capillary discharge for the Electrothermal (ET) or ET-chemical (ETC) launch system, one needs to solve the Saha equation to determine the composition of plasma for the transport coefficients. This would cause a relatively longer simulation runtime compared with conventional computational fluid dynamics problems. In this paper, the relatively difficult multidimensional problem of solving the Saha equation is transformed into a one-dimensional problem in the simulation of capillary discharge by constructing an iteration equation about temperature. A coefficient is introduced to ensure the convergence of this iteration equation. In order to improve the computational efficiency, this coefficient is further optimized and the methods of setting the iteration initial value dynamically are introduced. Several simulation tests are conducted to study the performance of these two methods. The results show that the simulation runtime could be significantly reduced with the methods presented in this paper.