CAJ | 학술논문

Bathe 算法将浸润面确定问题转变为常规的非线性本构问题，Signorini 条件将出溢面边界转化为常规的水头边界进行处理。由于非饱和渗流问题本身就是一个非线性渗透本构问题，将上述2种方法的联合使用，避免变分不等式的求解，在常规非线性有限元求解框架内做最小程度的改动基础上，实现饱和-非饱和渗流的求解，着重探讨以下几个问题：(1) Bathe方法收敛性的改善及其修正系数的三维推广；(2)适用渗流问题的Signorini条件边界交换算法及其实现；(3)提高非饱和非稳定渗流问题求解收敛性及质量守恒性的欠松弛处理方法。最后，通过典型的算例，讨论上述算法应用中的一些问题及其适用性和精度。
Bathe 산법장침윤면학정문제전변위상규적비선성본구문제，Signorini 조건장출일면변계전화위상규적수두변계진행처리。유우비포화삼류문제본신취시일개비선성삼투본구문제，장상술2충방법적연합사용，피면변분불등식적구해，재상규비선성유한원구해광가내주최소정도적개동기출상，실현포화-비포화삼류적구해，착중탐토이하궤개문제：(1) Bathe방법수렴성적개선급기수정계수적삼유추엄；(2)괄용삼류문제적Signorini조건변계교환산법급기실현；(3)제고비포화비은정삼류문제구해수렴성급질량수항성적흠송이처리방법。최후，통과전형적산례，토론상술산법응용중적일사문제급기괄용성화정도。
Bathe algorithm converts the locating of the phreatic surface to a nonlinear constitutive problem. And the implication of Signorini condition can simulate a seepage face as a head-fixed boundary through iterative calculation. Because an unsaturated seepage problem is also a nonlinear flow problem,the implication of Bathe algorithm and Signorini condition makes it possible to model both saturated and unsaturated seepage problems with a unified method by a minimal modification to an ordinary finite element method,and avoiding solving a variational inequality system. The followings are discussed mainly:(1) the improvements of Bathe algorithm in converge and its generalized form in a three-dimensional model;(2) the implement of the switching algorithm of Signorini condition to solving seepage problems;and (3) the under-relaxation scheme to improve the mass conservation and converge properties when an unsteady unsaturated problem is solved. Finally,some numerical examples are solved to evaluate the applicability of the proposed method;and the results are compared with those available in the literature.