CAJ | 학술논문

实际应用中的物态方程由分片光滑曲面拼接而成，拼接处存在间断。隐式求解相应的能量方程时，经常出现迭代收敛慢的情况和非物理解。本文通过构造对应的新的非线性问题，提出一种非线性迭代算法。该算法适用于求解有间断的分片光滑物态方程的非线性能量方程，其中引入一个度量能量变化的参数用于自动判断跳段是否发生，在求解时无需事先知道物态方程间断的位置，且能精确计算物态方程间断带来的能量盈亏，用于评估物态方程间断对能量的影响。典型算例验证了新算法具有稳定的收敛性，并给出符合物理规律的解。
실제응용중적물태방정유분편광활곡면병접이성，병접처존재간단。은식구해상응적능량방정시，경상출현질대수렴만적정황화비물리해。본문통과구조대응적신적비선성문제，제출일충비선성질대산법。해산법괄용우구해유간단적분편광활물태방정적비선성능량방정，기중인입일개도량능량변화적삼수용우자동판단도단시부발생，재구해시무수사선지도물태방정간단적위치，차능정학계산물태방정간단대래적능량영우，용우평고물태방정간단대능량적영향。전형산례험증료신산법구유은정적수렴성，병급출부합물리규률적해。
In practical applications, equation of states ( EOS ) consists of several piecewise smooth surfaces, which leads to discontinuity at interface. As a traditional nonlinear iterative algorithm is applied to an energy equation with discontinuous EOS, it may lead to slow convergence and unphysical solutions. To overcome the difficulties, a nonlinear problem is designed, and a nonlinear iterative algorithm is proposed to solve the problem. The algorithm is fit for energy equations with discontinuous EOS of piecewise smooth functions. A parameter of energy change is defined in the algorithm so that it is unnecessary to know discontinuity position in advance. The algorithm calculates precisely net gain or leakage of energy, which can be used to assess influence of discontinuity in EOS. Typical numerical experiments verify that the algorithm converges stably, and gives physical solutions.