We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different ve...We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically <em>Mathematica</em> [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.展开更多
The thrust coefficients and propulsive efficiency of a two-dimensional flexible fin with heaving and pitching motion were computed using FLUENT. The effect of different locations of the pitching axis on propulsive per...The thrust coefficients and propulsive efficiency of a two-dimensional flexible fin with heaving and pitching motion were computed using FLUENT. The effect of different locations of the pitching axis on propulsive performance was examined using three deflexion modes which are respectively, modified Bose mode, cantilever beam with uniformly distributed load and cantilever beam with non-uniformly distributed load. The results show that maximum thrust can be achieved with the pitching axis at the trailing edge, but the highest propulsive efficiency can be achieved with the pitching axis either 1/3 of the chord length from the leading edge in modified Bose mode, or 2/3 of the chord length from the leading edge in cantilever beam mode. At the same time, the effects of the Strouhal number and maximal attack angle on the hydrodynamics performance of the flexible fin were analyzed. Parameter interval of the maximum thrust coefficient and the highest propulsive efficiency were gained. If the Strouhal number is low, high propulsive efficiency can be achieved at low αmax , and vice versa.展开更多
Delaunay triangulation is gradually playing an important role in the field of finite element analysis, image recognition, and medical visualization.Considering the quality and partition efficiency, a new Delaunay tria...Delaunay triangulation is gradually playing an important role in the field of finite element analysis, image recognition, and medical visualization.Considering the quality and partition efficiency, a new Delaunay triangulation method based on constrained maximum circumscribed circle is proposed. First, according to two important criteria, the empty circle features and the maximized minimum angle characteristics, we established constrained conditions. Then, we iterated the container vertices, structure triangular face linked lists, and finally got the Delaunay data. The experimental results showed that the efficiency of the improved triangulation dissection method increased by 9.47% compared with traditional triangulation algorithms in irregular triangle vertex data.展开更多
In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constan...In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.展开更多
文摘We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically <em>Mathematica</em> [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.
基金Supported by the National Natural Science Foundation of China under Grant No.50879031
文摘The thrust coefficients and propulsive efficiency of a two-dimensional flexible fin with heaving and pitching motion were computed using FLUENT. The effect of different locations of the pitching axis on propulsive performance was examined using three deflexion modes which are respectively, modified Bose mode, cantilever beam with uniformly distributed load and cantilever beam with non-uniformly distributed load. The results show that maximum thrust can be achieved with the pitching axis at the trailing edge, but the highest propulsive efficiency can be achieved with the pitching axis either 1/3 of the chord length from the leading edge in modified Bose mode, or 2/3 of the chord length from the leading edge in cantilever beam mode. At the same time, the effects of the Strouhal number and maximal attack angle on the hydrodynamics performance of the flexible fin were analyzed. Parameter interval of the maximum thrust coefficient and the highest propulsive efficiency were gained. If the Strouhal number is low, high propulsive efficiency can be achieved at low αmax , and vice versa.
基金Supported by the National Natural Science Foundation of China(51179146)the Fundamental Research Funds for the Central Universities(2010-Ia-050,2011-IV-027)
文摘Delaunay triangulation is gradually playing an important role in the field of finite element analysis, image recognition, and medical visualization.Considering the quality and partition efficiency, a new Delaunay triangulation method based on constrained maximum circumscribed circle is proposed. First, according to two important criteria, the empty circle features and the maximized minimum angle characteristics, we established constrained conditions. Then, we iterated the container vertices, structure triangular face linked lists, and finally got the Delaunay data. The experimental results showed that the efficiency of the improved triangulation dissection method increased by 9.47% compared with traditional triangulation algorithms in irregular triangle vertex data.
基金supported by the Special Funds for Major State Basic Research Project(No.2005CB321701)
文摘In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.
