瞬态热传导问题的加权最小二乘无网格法

加权最小二乘无网格法是一种基于节点信息的纯无网格法,该方法使用最小二乘法建立系统的变分原理,通过移动最小二乘法构造近似函数,控制方程在节点处的残量使用最小二乘法予以消除,边界条件通过罚函数法引入。本文推导了瞬态热传导问题的加权最小二乘无网格计算格式,编制了相应的计算程序,算例结果表明,该方法具有精度高、前后处理简单的优点,是一种高效的的新型无网格法。

Meshless weighted least-square method for transient heat conduction problems

Meshless Weighted Least-Square Method(MWLS),which is only based on nodes' information.In MWLS the variation principle of system is constructed with weighted least-square residual method,and the approximation function is built by moving least-square method.The boundary conditions are enforced with a penalty function.Appling MWLS to solve transient heat conduction problems,the numerical results show that MWLS has several advantages such as high accuracy and easy for pre-process and post-process.