流动与传热数值计算中任意网格基架点下导数差分通式研究  

Study on Differential Equations Under Derivative of Arbitrary Mesh Node in Numerical Calculation of Flow and Heat Transfer

作　　者：宇波[1] 苏越 孙树瑜 焦开拓 陈宇杰 李敬法 YU Bo;SU Yue;SUN Shuyu;JIAO Kaituo;CHEN Yujie;LI Jingfa(Hydrogen Energy Research Center,School of Mechanical Engineering,Beijing University of Petrochemical Technology,Beijing 102617,China;School of Mechanical Engineering,China University of Petroleum,Beijing 102249,China;King Abdullah University of Science&Technology,Jeddah 21577,Saudi Arabia;School of Energy and Power Engineering,Xi'an Jiaotong University,Xi'an 710049,China)

机构地区：[1]北京石油化工学院机械工程学院并氢能研究中心,北京102617 [2]中国石油大学(北京)机械工程学院,北京102249 [3]阿卜杜拉国王科技大学,沙特吉达21577 [4]西安交通大学能源与动力工程学院,西安710049

出　　处：《工程热物理学报》2024年第7期2012-2018,共7页Journal of Engineering Thermophysics

基　　金：国家自然科学基金重点基金(No.51936001)。

摘　　要：在流动与传热数值计算中,导数离散一般是通过泰勒公式展开后应用待定系数法求解代数方程组得到。对于复杂网格基架,推导过程比较繁琐。为了解决这一问题,本文通过观察多组网格基架下节点上一二阶导数及截差的表达式,首先对通式形式进行了猜想,之后对节点上的导数及截差的通式给出了证明。对于任意网格基架下界面上一阶导数及截差的表达式,通过对拉格朗日插值求导化简得到。相比于传统方法,导数的差分通式的优点包括:1)避免了方程组的人工求解,节约计算时间;2)容易得到高精度的差分表达式;3)易于编制通用程序,基架点变化后无需对方程进行重新离散。本文推导的导数及截差的差分通式对于快速获取高精度的导数差分表达式具有一定的意义。In numerical calculation of flow and heat transfer,derivative discretization is generally obtained by using Taylor formula and undetermined coefficient method to solve algebraic equations.For complex grid frame,the derivation process is complicated.In order to solve this problem,by observing the expressions of the first and second derivative and the cut of the nodes under the grid frame,this paper first guesses the general formula,and then proves the general formula of the derivative and the cut of the nodes.The expressions of the first derivative and the cut on the lower interface of any grid frame are obtained by taking the derivative of Lagrange interpolation.Compared with the traditional method,the differential general formula of derivative has the following advantages:1)It avoids the manual solution of equations and saves calculation time;2)It is easy to obtain high-precision difference expressions;3)Easy to compile general program,no need to re-discretize the equation after the change of the base point.The general differential formula of derivative and intercept derived in this paper has certain significance for obtaining the differential expression of derivative quickly and accurately.

关 键 词：有限容积法 有限差分法 拉格朗日插值 导数差分表达式 

分 类 号：TE0[石油与天然气工程]