For flow simulations with complex geometries and structured grids,it is preferred for high-order difference schemes to achieve high accuracy.In order to achieve this goal,the satisfaction of free-stream preservation i...For flow simulations with complex geometries and structured grids,it is preferred for high-order difference schemes to achieve high accuracy.In order to achieve this goal,the satisfaction of free-stream preservation is necessary to reduce the numerical error in the numerical evaluation of grid metrics.For the linear upwind schemes with flux splitting the free-stream preserving property has been achieved in the early study[Q.Li et al.,Commun.Comput.Phys.,22(2017),pp.64–94].In the current paper,new series of nonlinear upwind-biased schemes through WENO interpolation will be proposed.In the new nonlinear schemes,the shock-capturing capability on distorted grids is achieved,which is unavailable for the aforementioned linear upwind schemes.By the inclusion of fluxes on the midpoints,the nonlinearity in the scheme is obtained through WENO interpolations,and the upwind-biased construction is acquired by choosing relevant grid stencils.New third-and fifth-order nonlinear schemes are developed and tested.Discussions are made among proposed schemes,alternative formulations of WENO and hybrid WCNS,in which a general formulation of center scheme with midpoint and nodes employed is obtained as a byproduct.Through the numerical tests,the proposed schemes can achieve the designed orders of accuracy and free-stream preservation property.In 1-D Sod and Shu-Osher problems,the results are consistent with the theoretical predictions.In 2-D cases,the vortex preservation,supersonic inviscid flow around cylinder at M¥=4,Riemann problem,and shock-vortex interaction problems have been tested.More specifically,two types of grids are employed,i.e.,the uniform/smooth grids and the randomized/locally-randomized grids.All schemes can get satisfactory results in uniform/smooth grids.On the randomized grids,most schemes have accomplished computations with reasonable accuracy,except the failure of one third-order scheme in Riemann problem and shock-vortex interaction.Overall,the proposed nonlinear schemes have the capability to solve flow problems on badly deformed grids,and the schemes can be used in the engineering applications.展开更多
For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of severa...For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of several meshless methods,which are more flexible and equally accurate numerical methods.The meshless method used in this work is the natural neighbour radial point interpolation method(NNRPIM).In order to discretize the problem domain,the NNRPIM only requires an unstructured nodal distribution.Then,using the Voronoi mathematical concept,it enforces the nodal connectivity and constructs the background integration mesh.The NNRPIM shape functions are constructed using the radial point interpolation technique.In this work,the displacement field of composite laminated plates is defined by high-order shear deformation theories.In the end,several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature.The obtained results show the efficiency and accuracy of the NNRPIM formulation.展开更多
基金sponsored by the project of National Numerical Wind-tunnel of China under the grant number No.NNW2019ZT4-B12The second author thanks for the support of National Natural Science Foundation of China under the Grant No.11802324The corresponding author thanks for the contribution of Dr.Qilong Guo on the incipient 1-D computations,and he is also grateful to Prof.Kun Xu for his efforts on the revision of the manuscript as well as Dr.Pengxin Liu for supplementary computations.
文摘For flow simulations with complex geometries and structured grids,it is preferred for high-order difference schemes to achieve high accuracy.In order to achieve this goal,the satisfaction of free-stream preservation is necessary to reduce the numerical error in the numerical evaluation of grid metrics.For the linear upwind schemes with flux splitting the free-stream preserving property has been achieved in the early study[Q.Li et al.,Commun.Comput.Phys.,22(2017),pp.64–94].In the current paper,new series of nonlinear upwind-biased schemes through WENO interpolation will be proposed.In the new nonlinear schemes,the shock-capturing capability on distorted grids is achieved,which is unavailable for the aforementioned linear upwind schemes.By the inclusion of fluxes on the midpoints,the nonlinearity in the scheme is obtained through WENO interpolations,and the upwind-biased construction is acquired by choosing relevant grid stencils.New third-and fifth-order nonlinear schemes are developed and tested.Discussions are made among proposed schemes,alternative formulations of WENO and hybrid WCNS,in which a general formulation of center scheme with midpoint and nodes employed is obtained as a byproduct.Through the numerical tests,the proposed schemes can achieve the designed orders of accuracy and free-stream preservation property.In 1-D Sod and Shu-Osher problems,the results are consistent with the theoretical predictions.In 2-D cases,the vortex preservation,supersonic inviscid flow around cylinder at M¥=4,Riemann problem,and shock-vortex interaction problems have been tested.More specifically,two types of grids are employed,i.e.,the uniform/smooth grids and the randomized/locally-randomized grids.All schemes can get satisfactory results in uniform/smooth grids.On the randomized grids,most schemes have accomplished computations with reasonable accuracy,except the failure of one third-order scheme in Riemann problem and shock-vortex interaction.Overall,the proposed nonlinear schemes have the capability to solve flow problems on badly deformed grids,and the schemes can be used in the engineering applications.
文摘For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of several meshless methods,which are more flexible and equally accurate numerical methods.The meshless method used in this work is the natural neighbour radial point interpolation method(NNRPIM).In order to discretize the problem domain,the NNRPIM only requires an unstructured nodal distribution.Then,using the Voronoi mathematical concept,it enforces the nodal connectivity and constructs the background integration mesh.The NNRPIM shape functions are constructed using the radial point interpolation technique.In this work,the displacement field of composite laminated plates is defined by high-order shear deformation theories.In the end,several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature.The obtained results show the efficiency and accuracy of the NNRPIM formulation.
