局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

移动加热器法生长碲锌镉晶体的组分输运与界面形貌研究

移动加热器法(THM)生长碲锌镉晶体时,界面稳定性对晶体生长的质量有很大影响。本文基于多物理场有限元仿真软件Comsol建立了THM生长碲锌镉晶体的数值模拟模型,讨论了Te边界层与组分过冷区之间的关系,对不同生长阶段的物理场、Te边界层与组分过冷区进行仿真研究,最后讨论了微重力对物理场分布的影响,并对比了微重力与正常重力下的生长界面形貌。模拟结果表明,Te边界层与组分过冷区的分布趋势是一致的,在不同生长阶段,流场中次生涡旋的位置会发生移动,从而导致生长界面的形貌随着生长的进行发生变化,同时微重力条件下形成的生长界面形貌最有利于单晶生长。因此,在晶体生长的中前期,对次生涡旋位置的控制和对组分过冷的削弱,是THM生长高质量晶体的有效方案。     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.