潜蚀的局部守恒有限元和有限体积交替解法
Staggered finite element and finite volume method for suffusion simulation based on local conservation
王刚 1邓泽之 2金伟 3张建民4
作者信息
- 1. 重庆大学山地城镇建设与新技术教育部重点实验室,重庆 400045;重庆大学土木工程学院,重庆 400045
- 2. 重庆大学土木工程学院,重庆 400045
- 3. 中国电建集团成都勘测设计院有限公司,四川成都 610072
- 4. 清华大学土木水利学院,北京 100084
- 折叠
摘要
潜蚀的模拟需要计算土中的渗流过程以及土中细粒随孔隙水流的运移过程.常规有限元法在求解纯运移方程时存在稳定性问题,为此提出了一个采用有限元法求解渗流方程、有限体积法求解细粒运移方程的交替方法.鉴于常规有限元法不能给出满足有限体积法输入要求的流速场,给出了一个基于单元不平衡流量总体再平衡修正单元边界流速的算法.利用该算法对有限元计算的单元边界流速进行局部守恒处理,即可实现在同一有限元网格上利用有限体积法求解细粒运移方程,因此可以方便地和现有的有限元计算程序结合.算例验证表明,所提出的局部守恒处理算法及交替解法计算效率高且具有可接受的精度,是模拟潜蚀问题的一条简单实用的途径.
Abstract
Simulating suffusion involves computing both the seepage flow of pore water in soil and the transport of fine particles with pore water flow.Since the conventional finite element method(FEM)exhibits instability when used to solve the pure transport equations,a staggered method that employs FEM to solve the seepage equation and the finite volume method(FVM)for the particle transport equation is proposed.As conventional FEM cannot provide a locally conservative velocity field that satisfies the input requirement of FVM,an algorithm,based on the global re-balance of the element residual fluxes,is employed to correct the flow velocity at element boundaries.With this algorithm,the local conservation of the flow velocity computed by FEM at the element boundary is achieved.This enables FVM to solve the particle transport equation on the same FEM mesh,facilitating the convenient integration of FVM with existing FEM codes.Case studies demonstrate that the proposed local conservation algorithm and the staggered method exhibit high computational efficiency and acceptable accuracy,offering a straightforward and practical approach to simulating suffusion problems.
关键词
潜蚀/渗流/有限元法/有限体积法/局部守恒Key words
suffusion/seepage/finite element method/finite volume method/local conservation引用本文复制引用
基金项目
国家自然科学基金(52079012)
重庆市自然科学基金(cstc2021 jcyjimsxmX0598)
出版年
2024
国家科技期刊平台
NSTL
万方数据