In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in ...In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.展开更多
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...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.展开更多
基金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)+2 种基金The research of Guanghui Hu was partially supported by the FDCT of the Macao S.A.R.(0082/2020/A2)the National Natural Science Foundation of China(Grant Nos.11922120,11871489)the Multi-Year Research Grant(2019-00154-FST)of University of Macao,and a Grant from Department of Science and Technology of Guangdong Province(2020B1212030001).
文摘In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.
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)+4 种基金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 Macaoa grant from Department of Science and Technology of Guangdong Province(2020B1212030001).
文摘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.
