基于三维管道模型的快速边界元法在阴极保护分析中的应用

Fast boundary element method based on a 3D pipe model for analyzing cathodic protection

该文采用边界元法(BEM)对包含大规模管道结构的阴极保护系统进行分析。为降低管道上的单元数量和单元积分计算量,提出一种三维管道边界元模型,将管道离散为线单元且保留管道圆柱面积分。为了能够在普通微机上模拟大规模阴极保护系统,使用快速多极算法(FMM)加速边界元方程的求解。针对阴极极化边界条件引入的非线性问题,采用迭代算法求解。数值算例表明:采用该文线单元离散管道,相比常规三角形单元,可将单元数量降低一个数量级;快速多极算法可以求解自由度为50 000量级的大规模阴极保护问题。

The boundary element method（BEM）was used to analyze a cathodic protection（CP）system consisting of large pipeline structures.A three-dimensional pipe boundary element model was used to reduce the number of elements on the pipelines as well as the element integral computations.The pipelines were meshed with line elements with the boundary integrals were based on the original shapes.The large-scale CP problem was solved on a common desktop computer using the fast multipole method（FMM）to accelerate the BEM.The nonlinearity introduced by the polarization curve at the cathode was solved iteratively.The numerical results demonstrate that the number of elements can be reduced by one order of magnitude when discretizing pipelines with these line elements compared with triangular elements and that the FMM can solve large CP problems with up to 50 000 dimension of freedoms（DOFs）.