CAJ | 학술논문

本文基于经典的有限体积方法，讨论了带有间断系数二维椭圆型方程的求解问题。文中通过在求解椭圆型方程时截取通量函数的更多项泰勒展开式，同时结合有限差分方法对与边界相邻的网格点进行特殊处理，改进了间断系数的求解方法，得到了一种修正的有限体积方法，该方法在界面处是一阶精度，但方法整体可达到二阶精度。数值实验表明，文中构造的修正有限体积方法是有效的。
본문기우경전적유한체적방법，토론료대유간단계수이유타원형방정적구해문제。문중통과재구해타원형방정시절취통량함수적경다항태륵전개식，동시결합유한차분방법대여변계상린적망격점진행특수처리，개진료간단계수적구해방법，득도료일충수정적유한체적방법，해방법재계면처시일계정도，단방법정체가체도이계정도。수치실험표명，문중구조적수정유한체적방법시유효적。
Based on classical finite volume method for solving two dimensional elliptic equation with discontinuous e?cient, a modified finite volume method is presented in this paper. The finite difference method is cooperated with for dealing with some grid point around boundary, and more Taylor expansion items of flux function are intercepted in order to obtain higher numerical accuracy. There is first order accuracy at interface and second order accuracy in the whole domain. Numerical results indicate that the modified finite volume method is effective.