A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,...A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,and dispersion characteristics are achieved using appropriate values of the parameter.The proposed scheme has second-order accuracy with and without physical damping.Moreover,its stability,accuracy,and dispersion are analyzed.In addition,its performance is demonstrated by the two-dimensional scalar wave problem,the single-degree-of-freedom problem,two degrees-of-freedom spring system,and beam with boundary constraints.The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme.When the proposed scheme is applied to solve the wave problem,more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter.For the single-degree-offreedom system,two degrees-of-freedom system,and the time responses of beam,the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.展开更多
The accurate computation of different turbulent statistics poses different requirements on numerical methods.In this paper,we investigate the capabilities of two representa-tive numerical schemes in predicting mean ve...The accurate computation of different turbulent statistics poses different requirements on numerical methods.In this paper,we investigate the capabilities of two representa-tive numerical schemes in predicting mean velocities,Reynolds stress and budget of turbulent kinetic energy(TKE)in low Mach number flows.With concerns on numeri-cal order of accuracy,dissipation and dispersion properties,a high-order upwind scheme with relatively good dispersion and dissipation and a second-order non-dissi-pative central scheme with perfect dissipation but poor dispersion are adopted for this comparative study.By carrying out a series of numerical simulations including Taylor-Green vortex,turbulent channel flow at Reτ=180 and turbulent flow over periodic hill at Reb=10595,it can be obtained that although the high-order upwind scheme lacks perfection of dissipation in high wave number range,it still demonstrates superior predictive capability compared with the second-order non-dissipative central scheme,especially with relatively coarse grids.Finally,by taking the high-order upwind scheme as a suitable selection for turbulence simulation,the turbulent flow over a 30P30N multi-element airfoil is investigated as an application study.After briefly comparing the simulated profiles and spectrum with reference experimental results as validation,the budget of TKE is analyzed to locate the dominant flow structures and regions.It is found that the production and dissipation terms behave in a“monopole”pattern in the locations with strong shears and wakes.Whereas the advection and diffusion terms show an“inward”pattern and an“outward”pattern,which indicate the spatial transport of TKE between the center of the shear layer and nearby locations.展开更多
文摘A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,and dispersion characteristics are achieved using appropriate values of the parameter.The proposed scheme has second-order accuracy with and without physical damping.Moreover,its stability,accuracy,and dispersion are analyzed.In addition,its performance is demonstrated by the two-dimensional scalar wave problem,the single-degree-of-freedom problem,two degrees-of-freedom spring system,and beam with boundary constraints.The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme.When the proposed scheme is applied to solve the wave problem,more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter.For the single-degree-offreedom system,two degrees-of-freedom system,and the time responses of beam,the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.
基金This work is supported by the National Natural Science Foundation of China(Nos.12102360,92152301)the Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-QN-0017).
文摘The accurate computation of different turbulent statistics poses different requirements on numerical methods.In this paper,we investigate the capabilities of two representa-tive numerical schemes in predicting mean velocities,Reynolds stress and budget of turbulent kinetic energy(TKE)in low Mach number flows.With concerns on numeri-cal order of accuracy,dissipation and dispersion properties,a high-order upwind scheme with relatively good dispersion and dissipation and a second-order non-dissi-pative central scheme with perfect dissipation but poor dispersion are adopted for this comparative study.By carrying out a series of numerical simulations including Taylor-Green vortex,turbulent channel flow at Reτ=180 and turbulent flow over periodic hill at Reb=10595,it can be obtained that although the high-order upwind scheme lacks perfection of dissipation in high wave number range,it still demonstrates superior predictive capability compared with the second-order non-dissipative central scheme,especially with relatively coarse grids.Finally,by taking the high-order upwind scheme as a suitable selection for turbulence simulation,the turbulent flow over a 30P30N multi-element airfoil is investigated as an application study.After briefly comparing the simulated profiles and spectrum with reference experimental results as validation,the budget of TKE is analyzed to locate the dominant flow structures and regions.It is found that the production and dissipation terms behave in a“monopole”pattern in the locations with strong shears and wakes.Whereas the advection and diffusion terms show an“inward”pattern and an“outward”pattern,which indicate the spatial transport of TKE between the center of the shear layer and nearby locations.
