Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh...Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.展开更多
In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & d...In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & diffusion equation, on the one hand, the advection term itself has the strong unilateral property, which means information in the upper reaches is transmitted downstream via the advection term; on the other hand, because of the opposite direction of calculation, it is essential for information to be conveyed upstream by means of the advection term. In addition, unlike that in the forward calculation, the diffusion term in the backward calculation is prone to accumulate errors, and thus renders the whole scheme unstable. Therefore, we adopt the central difference to deal with both the convectional term and the diffusion term. By examining two practical examples (1) under the unlimited boundary condition, and (2) under the limited boundary condition, it is proven that this method could achieve fundamentally satisfactory results not only in the open ocean but also in the closed or semi-closed bay.展开更多
文摘Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.
基金funded by NSFC 40076005 and Frontier Innovation Project L390221103 from the Chinese Academy of Sciencesthe financial support from the National Tenth Five-Year Key Project H57022113.
文摘In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & diffusion equation, on the one hand, the advection term itself has the strong unilateral property, which means information in the upper reaches is transmitted downstream via the advection term; on the other hand, because of the opposite direction of calculation, it is essential for information to be conveyed upstream by means of the advection term. In addition, unlike that in the forward calculation, the diffusion term in the backward calculation is prone to accumulate errors, and thus renders the whole scheme unstable. Therefore, we adopt the central difference to deal with both the convectional term and the diffusion term. By examining two practical examples (1) under the unlimited boundary condition, and (2) under the limited boundary condition, it is proven that this method could achieve fundamentally satisfactory results not only in the open ocean but also in the closed or semi-closed bay.
