非线性双曲线固结方程的精细积分解法

Precise integration solution method of nonlinear hyperbolic consolidation equation

为解决传统有限差分法在求解固结方程时关于时间步长选取对解的稳定性和收敛性影响问题,针对固结系数不为常数的一维非线性双曲线固结方程求解,提出一种采用精细积分法进行时间离散的数值解法。详细推导该方法的具体求解过程,并结合工程实例,将精细积分解法与传统有限差分解法进行对比。结果表明,精细积分解法不受时间步长取值大小的限制,具有良好的计算精度和数值稳定性。

In order to solve the problem that the solution stability and convergence are influenced by time step selection in solving consolidation equation by typical finite difference method,aiming at the solution of one-dimensional nonlinear hyperbolic consolidation equation with non-constant consolidation coefficient,we put forward a numerical solution with time discretization by precise integration method,derive the solving process of this method in detail,and compare the precise integration solution with the typical finite difference solution combining with engineering example.The results show that the precise integration method is not limited by the time step size,and has good accuracy and numerical stability.