A WKB analysis of the buckling condition for a cylindrical shell of arbitrary thickness subjected to an external pressure

We consider the plane-strain buckling of a cylindrical shellof arbitrary thickness which is made of a Varga material andis subjected to an external hydrostatic pressure on its outersurface. The WKB method is used to solve the eigenvalue problemthat results from the linear bifurcation analysis. We show thatthe circular cross-section buckles into a non-circular shapeat a value of µ₁ which depends on A₁/A₂ and a mode number,where A₁ and A₂ are the undeformed inner and outer radii, andµ₁ is the ratio of the deformed inner radius to A₁. Inthe large mode number limit, we find that the dependence ofµ₁ on A₁/A₂ has a boundary layer structure: it is constantover almost the entire region of 0 < A₁/A₂ < 1 and decreasessharply from this constant value to unity as A₁/A₂ tends tounity. Our asymptotic results for A₁ – 1 = O(1) and A₁– 1 = O(1/n) are shown to agree with the numerical resultsobtained by using the compound matrix method.     

对求解非线性方程方法的探索

BaiCL在2001年提出了双曲函数法，并把解设成具体的双曲函数，即sinhw和coshw的线性组合．本文把解设成是由2个函数f(ξ)和g(ξ)组成的线性组合，它们可以有多种取法，从而使方程更直接、更有效．借助数学软件Maple，用改进后的方法和吴文俊消元法，求解Bai C L文中的一个例子，获得了包含Bai文结果在内的更为丰富、精确的行波解．     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

CAP-子群与p-幂零性

设G是有限群。H是G的一个正规子群。P是|H|的一个素因子。P是H的一个Sylow p-子群。若下列条件之一满足。则H是p-幂零：1)P的极大子群都是G的CAP-子群且(|H|，P-1)=1；2)P的二次极大子群都是G的CAP-子群且(|H|，P^2-1)=1。特别地，若进一步假设G／H为P-幂零且(|G|，P-1)=1或(|G|，P^2-1)=1。则G自身亦为P-幂零。     

Direct numerical simulation of settling of a large solid particle during bioconvection

Settling of a large solid particle in bioconvection flow caused by gyrotactic microorganisms is investigated. The particle is released from the top of the bioconvection chamber; its settling pattern depends on whether it is released in the centre of the bioconvection plume or at its periphery. The Chimera method is utilized; a subgrid is generated around a moving particle. The method suggested by Liu and Wang (Comput. Fluid 2004; 33 :223–255) is further developed to account for the presence of a moving boundary in the streamfunction‐vorticity formulation using the finite‐difference method. A number of cases for different release positions of the particle are computed. It is demonstrated that bioconvection can either accelerate or decelerate settling of the particle depending on the initial position of the particle relative to the plume centre. It is also shown that the particle impacts bioconvection plume by changing its shape and location in the chamber. Copyright © 2005 John Wiley & Sons, Ltd.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

A parallel cell‐based DSMC method on unstructured adaptive meshes

A parallel DSMC method based on a cell‐based data structure is developed for the efficient simulation of rarefied gas flows on PC‐clusters. Parallel computation is made by decomposing the computational domain into several subdomains. Dynamic load balancing between processors is achieved based on the number of simulation particles and the number of cells allocated in each subdomain. Adjustment of cell size is also made through mesh adaptation for the improvement of solution accuracy and the efficient usage of meshes. Applications were made for a two‐dimensional supersonic leading‐edge flow, the axi‐symmetric Rothe's nozzle, and the open hollow cylinder flare flow for validation. It was found that the present method is an efficient tool for the simulation of rarefied gas flows on PC‐based parallel machines. Copyright © 2004 John Wiley & Sons, Ltd.     

A time‐accurate pseudo‐compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation

A preconditioning approach based on the artificial compressibility formulation is extended to solve the governing equations for unsteady turbulent reactive flows with heat release, at low Mach numbers, on an unstructured hybrid grid context. Premixed reactants are considered and a flamelet approach for combustion modelling is adopted using a continuous quenched mean reaction rate. An overlapped cell‐vertex finite volume method is adopted as a discretisation scheme. Artificial dissipation terms for hybrid grids are explicitly added to ensure a stable, discretised set of equations. A second‐order, explicit, hybrid Runge–Kutta scheme is applied for the time marching in pseudo‐time. A time derivative of the dependent variable is added to recover the time accuracy of the preconditioned set of equations. This derivative is discretised by an implicit, second‐order scheme. The resulting scheme is applied to the calculation of an infinite planar (one‐dimensional) turbulent premixed flame propagating freely in reactants whose turbulence is supposed to be frozen, homogeneous and isotropic. The accuracy of the results obtained with the proposed method proves to be excellent when compared to the data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.