A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions

In this paper, we present a unified finite volume method preserving discrete maximum principle (DMP) for the conjugate heat transfer problems with general interface conditions. We prove the existence of the numerical solution and the DMP-preserving property. Numerical experiments show that the nonlinear iteration numbers of the scheme in [24] increase rapidly when the interfacial coefficients decrease to zero. In contrast, the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero, which reveals that the unified scheme is more robust than the scheme in [24]. The accuracy and DMP-preserving property of the scheme are also veried in the numerical experiments.     

A higher-order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions

We propose a hybrid numerical scheme to discretize a class of singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions on an equidistributed grid. The hybrid difference scheme is developed by using a modified backward difference scheme in time, a combination of the cubic spline and exponential spline difference scheme in space. The proposed scheme uses a cubic spline difference scheme for the discretization of robin-boundary conditions. For the time discretization of the problem, we use the standard uniform mesh while a layer adapted equidistributed grid is generated for the spatial discretization. By equidistributing a curvature-based monitor function, the spatial adaptive grid is able to capture the presence of parabolic boundary layers without using any prior information about the solution. Parameter uniform error estimates are derived to illustrate an optimal convergence of first-order in time and second-order in space for the proposed discretization. The accuracy of the proposed scheme is confirmed by the numerical experiments that underpin the theoretical analysis.     

非紧空间上折现Hamilton-Jacobi方程粘性解的存在性讨论*

当底空间紧时, 初始函数为连续函数的Lax-Oleinik型粘性解是局部半凹的,所以是相应的Hamilton-Jacobi\ (以下简称为H-J) 演化方程(简称为接触H-J方程)的粘性解.当底空间非紧时, 对于H-J方程和接触H-J方程, 其Lax-Oleinik型解的下确界未必能取到.文章将探讨在非紧空间上, 折现H-J方程粘性解有限性的条件, 并给出了在此假设下粘性解的表达式.     

Difference Independence of the Euler Gamma Function*

In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma function Г. More precisely,if P is a polynomial of n+1 variables in C[X,Y₀,…,Y_n-1] such that P(s,Г(s+a₀),…,Г(s+a_n-1))≡0 for some(a₀,…,a_n-1) ∈ Cⁿ and a_i-a_j ■ Z for any 0≤i相似文献   

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

粘性可压混合层时间稳定性对称紧致差分求解

基于可压扰动方程组的一阶改型 ,将高精度对称紧致格式引入边值法数值线性稳定性分析。对所获非线性离散特征值问题给出了一个通用形式二阶迭代局部算法 ,实现了时间模式和空间模式的统一求解 ,并将扰动特征值及其特征函数同时得到。据此分析了可压平面自由混合层时间稳定性 ,涉及二维 /三维扰动波、粘性 /无粘扰动波、第一 /第二模态、特征函数、伪特征值谱等。研究表明 ,压缩性效应和粘性效应对最不稳定扰动波数和增长率呈相似的减抑作用 ;在 Mc=1附近 ,从高波数段开始 ,粘性效应可强化二维不稳定扰动波由第一模态向第二模态的过渡     

Energy release rates in a constrained epoxy disc with Hookean and Mooney–Rivlin materials

Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composite body is uniformly raised. It is found that the linear and the nonlinear analyses give qualitatively similar results for the two loadings. For each load, the energy release rate increases with an increase in the starter crack length, reaches a maximum value and then decreases gradually.     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

On the bursting of linear polymer melts in inflation processes

Molten LLDPE and HDPE plates (thickness 2 mm) have been inflated into a circular cylinder (inner radius 31 mm) under isothermal conditions. Low deformation rates allow the plates to be inflated considerably into the cylinder, and at high inflation rates an early burst is observed.Axis-symmetric numerical simulation of the inflations have been performed, using a constitutive equation in the form of a separable memory integral where the strain dependence is described by the Linear Molecular Stress Function (L-MSF) model with dissipative convective constraint release. The material parameters in the constitutive model are obtained using liner viscoelastic (oscillatory shear) and uni-axial elongational measurements.The numerical simulations were performed for inflation of a flat plate and a perturbed plate, where a small circular cone was removed from the centre of the surface of the plate. This was done in order to investigate the stability of the inflations. It is shown that all of the inflations are hydrodynamically unstable, though the effect on the occurrence of the burst is limited. One exception is at slow inflation, where an unexpected burst may appear as a consequence of minute deviations from an ideal flat plate. All of the numerical calculations show quantitative agreement with the experiments for a wide range of experimental conditions. This strongly suggests that the initiation of the burst is a hydrodynamic phenomenon.The critical parameters in the inflation of molten linear polymers have been investigated using the Gel equation as a memory function (M(s)=Ans ^–(1+n)) and inflating the plate with a constant velocity for the top of the plate. The hydrodynamic burst in a linear polymer is mainly associated with the linear viscoelastic properties and only slightly with the non-linear strain dependence. Increased (linear) elasticity reduces the inflated volume, at the same inflation velocity, before the burst occurs. Furthermore, the critical parameter for the occurrence of the burst (whether or not the burst occurs) is related to the crossover point (G=G) in linear viscoelasticity.     

Compact finite difference-Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported. The project supported by the National Natural Science Foundation of China