Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential eq...Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential equations. Methods and the basic lemmas; Analysis of convergence and stability.展开更多
This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical stabilit...This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical stability of onestep Runge-Kutta methods, we obtain that a multistep Runge-Kutta method for DDEs is stable iff the corresponding methods for ODEs is A-stable under suitable interpolation conditions.展开更多
Ship bow wave breaking contains complex flow mechanism,which is very important for ship performance.In this study,a practical numerical simulation scheme for bow wave breaking is proposed and the scheme is applied to ...Ship bow wave breaking contains complex flow mechanism,which is very important for ship performance.In this study,a practical numerical simulation scheme for bow wave breaking is proposed and the scheme is applied to the simulation of bow wave breaking of KCS ship model with Fr=0.26,0.30,0.35,0.40,analyzing the impact of speed on the bow wave breaking.The results indicate that an increase in speed leads to a significant rise in viscous pressure resistance and more pronounced bow wave breaking.Moreover,it is found that the traditional wave height function in OpenFOAM is not suitable for detailed studies of bow wave breaking.This study extracts different free surfaces through top and bottom views to further analyze the free surface overturning,droplet splashing,and cavity entrainment in bow wave breaking.Additionally,the spatial and temporal distribution of cavities at Fr=0.40 is analyzed,revealing that cavity distribution is closely related to vortex structures and exhibits a periodic pulsation characteristic of approximately 12 s.展开更多
Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly...Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6.展开更多
基金National Natural Science Foundation of China!No.69974018 Postdoctoral Science Foundation of China.
文摘Presents information on a study which dealt with the error behavior and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation as applied to the nonlinear delay differential equations. Methods and the basic lemmas; Analysis of convergence and stability.
基金the National Natural Science Foundation of China (No.69974018).
文摘This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical stability of onestep Runge-Kutta methods, we obtain that a multistep Runge-Kutta method for DDEs is stable iff the corresponding methods for ODEs is A-stable under suitable interpolation conditions.
基金Project supported by the National Natural Science Foundation of China(Grant No.52131102).
文摘Ship bow wave breaking contains complex flow mechanism,which is very important for ship performance.In this study,a practical numerical simulation scheme for bow wave breaking is proposed and the scheme is applied to the simulation of bow wave breaking of KCS ship model with Fr=0.26,0.30,0.35,0.40,analyzing the impact of speed on the bow wave breaking.The results indicate that an increase in speed leads to a significant rise in viscous pressure resistance and more pronounced bow wave breaking.Moreover,it is found that the traditional wave height function in OpenFOAM is not suitable for detailed studies of bow wave breaking.This study extracts different free surfaces through top and bottom views to further analyze the free surface overturning,droplet splashing,and cavity entrainment in bow wave breaking.Additionally,the spatial and temporal distribution of cavities at Fr=0.40 is analyzed,revealing that cavity distribution is closely related to vortex structures and exhibits a periodic pulsation characteristic of approximately 12 s.
基金supported by the National Natural Science Founation of China(Grant No.11572350)
文摘Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6.
