控制体有限元中插值函数特性比较与算例分析  

Comparison of Interpolation Functions in Control Volume Finite Element Method and Numerical Analysis

作　　者：宋宇[1] 曹树良[1] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《农业机械学报》2012年第7期79-84,共6页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金资助项目(51176088)

摘　　要：探讨了求解不可压流动问题的控制体有限元方法,提出了流线FCBI构造插值函数的方法,并与传统FCBI和推广FCBI方法进行比较。选择方腔流动和S型管道流动两个经典算例,分析讨论了3种插值函数在求解不同流动问题时的共性与特性。结果表明:对对流占优的流动问题,尤其是流动较为复杂的对流占优问题,流线FCBI插值函数能更好地描述单元中速度的分布,较其他两种插值函数更容易获得稳定的收敛解;对非对流占优的流动问题,当单元Re小于5时,3种插值函数均能获得较精确的计算结果,但当单元Re数较高时,3种插值函数的精度均较低。Control volume finite element method to solve incompressible flow problems was investigated.The streamline FCBI method was built and compared with the original FCBI and general FCBI method.Lid-driven cavity flow and S-channel flow were chosen as the test cases.The similarities and differences among the three interpolation functions were discussed according to the analysis.The results showed that for convection-dominated flow,especially with complex performances,the Streamline FCBI method could better describe the velocity distributions in the element and achieve more stable converged results.For convection-diffusion problems,the precision of all the methods were low when element Re was high.From the analysis that for convection-diffusion problems,it is concluded that good results can be achieved by using FCBI methods when element Re is less than 5.

关 键 词：不可压流动 控制体 有限元方法 插值函数 管道流 

分 类 号：O242.21[理学—计算数学] O357.1[理学—数学]