毛细滞回内变量模型的高效数值积分方法  

An Efficient Numerical Integration Method for the Capillary Hysteresis Internal Variable Model

作　　者：李文涛[1] 韦昌富[1] 马田田[1] 

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,武汉430071

出　　处：《应用数学和力学》2013年第8期863-870,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11072255);广西自然科学基金资助项目(2011GXNSFE018004)

摘　　要：毛细滞回内变量模型是基于热动力学基本原理推导出来的土水特征本构模型,能够有效地描述干湿循环情况下非饱和土中的毛细滞回现象.研究了该模型的形式特点和数值积分方法,就经典的Euler法、4阶Runge-Kutta法和4阶Adams-Bashforth法的积分效果进行了对比.计算结果表明,Euler法精度很低,累计误差较大;4阶Adams-Bashforth法精度最高,且运算效率高于同阶的Runge-Kutta法,适合对该模型进行求解和参数标定.将基于Adams-Bashforth法的子程序集成到有限元程序中,两相渗流模拟结果的精度有了较大提高.Derived from thermo dynamic principle,the capillary hysteresis internal variable model is capable of describing the capillary hysteretic phenomena in unsaturated soils.The mathematical characteristics of this model were studied,followed by a numerical experimentation with classical Euler method,fourth-order Runge-Kutta method and fourth-order Adams-Bashforth method.The results show that Euler method has lower accuracy and larger accumulated error,whereas Adams-Bashforth method holds the upper most accuracy and the better efficiency compared with the same order Runge-Kutta method and is suitable for the solution and calibration of the internal variable model.Moreover,Adams-Bashforth method is implemented into the finite element programme,leading to more accurate results in simulation of two-phase flow.

关 键 词：毛细滞回 内变量 数值积分 两相流 非饱和土 

分 类 号：TU411[建筑科学—岩土工程] O348[建筑科学—土工工程]