ANURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented h-Adaptivity  

作　　者：Xucheng Meng Guanghui Hu 

机构地区：[1]Research Center for Mathematics,Beijing Normal University,Zhuhai 519087,China [2]BNU-HKBU United International College,Zhuhai 519087,China [3]Department of Mathematics,University of Macao,Macao SAR,China [4]ZhuhaiUMScience and Technology Research Institute,Zhuhai,Guangdong Province,China [5]Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Dynamics and Engineering Applications,University of Macao,Macao SAR,China

出　　处：《Communications in Computational Physics》2022年第7期490-523,共34页计算物理通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12101057);the Scientific Research Fund of Beijing Normal University(Grant No.28704-111032105);the Start-up Research Fund from BNU-HKBU United International College(Grant No.R72021112);supported by FDCT of the Macao S.A.R.(0082/2020/A2);National Natural Science Foundation of China(Grant Nos.11922120,11871489);the Multi-Year Research Grant(MYRG2020-00265-FST)of University of Macao;a grant from Department of Science and Technology of Guangdong Province(2020B1212030001).

摘　　要：In[A NURBS-enhanced finite volume solver for steady Euler equations,X.C.Meng,G.H.Hu,J.Comput.Phys.,Vol.359,pp.77–92],aNURBS-enhanced finite volume method was developed to solve the steady Euler equations,in which the desired high order numerical accuracy was obtained for the equations imposed in the domain with a curved boundary.In this paper,the method is significantly improved in the following ways:(i)a simple and efficient point inversion technique is designed to compute the parameter values of points lying on a NURBS curve,(ii)with this new point inversion technique,the h-adaptive NURBS-enhanced finite volume method is introduced for the steady Euler equations in a complex domain,and(iii)a goal-oriented a posteriori error indicator is designed to further improve the efficiency of the algorithm towards accurately calculating a given quantity of interest.Numerical results obtained from a variety of numerical experiments with different flow configurations successfully show the effectiveness and robustness of the proposed method.

关 键 词：Steady Euler equations NURBS-enhanced finite volume method goal-oriented a posteriori error estimation non-oscillatory k-exact reconstruction point inversion 

分 类 号：O17[理学—数学]