中文摘要：

本文使用直接配点无网格法结合共轭梯度法对管道内壁面侵蚀状况进行了反演识别。直接配点无网格法使用节点离散求解区域,采用移动最小二乘近似构造试函数,直接配点法构造线性方程组进行导热正问题求解;反演过程采用共轭梯度法使目标函数最小化,Akima三次样条插值将连续的几何边界反演问题转化为离散点几何位置的反演,并最终将这些离散点拟合成为光滑曲线。文中选择两个典型算例对数值方法进行验证,模拟结果表明使用直接配点无网格法结合共轭梯度法进行管道内壁几何边界识别具有较高精度。

英文摘要：

A geometry identification problem of pipeline＇s inner boundary is solved by using direct collocation meshless method and the conjugate gradient method.A number of collocation points are taken to discretize the interested domain,and the moving least-square approximation is employed to construct the trial function.The identification results are obtained through minimizing the objective function by using conjugate gradient method.Akima cubic interpolation is employed to transform the geometry boundary inverse problem to the discrete boundary points＇ inverse problem and approximate the unknown boundary in inverse iterative process.In order to illustrate the performance and verify the new solution method,two typical cases are considered in this work.The numerical results show that the direct collocation meshless method combined with conjugate gradient method is accurate and stable for solving geometry identification problem of pipeline＇s inner boundary.