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

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.

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