A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations （CDEs） is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.     

运动水平平板上混合对流的群论分析

本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析，得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布，同时壁面运动速度正比于X(3-n)／(7-5n)时存在相似性解．导出了相似性解方程，用四阶Runge－Kutta方法进行了计算，给出了Pr＝0．72　和Sc，K1，K2，K3参数下的速度、温度和浓度分布，得出了各参数对流场、温度场的影响。     

不用Kirchhoff—Love假定的三维弹性板近似理论及其边界条件

红典弹性板理论采用了著名的克希霍夫（Ｋｉｒｃｈｈｏｆｆ）－拉甫（Ｌｏｖｅ）的经典基本假定，在卡氏张量坐标ｘｉ（ｉ＝０，１，２）中，这些基本假定是：（１）略去横向即Ｘ０轴向正应变，即假定ｅ００＝０；（２）略去横向剪应变，即假定ｅ０ａ＝０，其中ａ＝１，２；（３）略去横向正应力，即假定σ００＝０。人们利用这些假定，建立了应变位移关系和应力位移关系，再利用应力平衡的三维方程，通过跨厚度的积分，找到弹性板中     

带对流的稳态Stefan问题的有限元逼近

关于带有对流情形的稳态Stefan问题,其中假设液相部分的流动由Stokes方程确定,Canon,DiBennedetto,Knightly曾作过理论研究.本文将讨论其有限元逼近问题,并且得到了在合理正则性假设下的误差估计.     

Acoustic scattering from multiple spheres by using a kind of addition formulae for the spherical wave functions

A kind of addition formulae for the spherical wave functions is generated by using the bicentric expansion of Green function in spherical coordinates. For an acoustical system with multiple spheres, the addition formulae permit the field expansions all referred to the center of one of the spheres, whose boundary conditions can be consequently used to study the multiple scattering easily. The two-sphere acoustical system with different boundary conditions is considered and the field scattered by each sphere can be obtained by solving an infinite set of two linear, complex, algebraic equations, whose coefficients are coupled through double sums in the spherical wave functions. Finally, the form functions of two spheres insonified by a plane wave at arbitrary angles of incidence are calculated and the addition formulae presented are validated by comparing the corresponding numerical results with those of the existing literature.     

Smooth Transition from Shakura—Sunyaev Disc to Advection—Dominated Accretion Flow

We solve a set of basic equations describing black hole accretion flows using the standard Runge-kutta method and a bridging formula for the radiative cooling,and show that a smooth transition from a shakura-Sunyaev disc to an advection-dominated accretion flow is realizable for the high-viscosity case,without the need of involving any extra mechanism of energy transport.     

一类非定常对流占优扩散问题差分-流线扩散法的后处理

讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD),利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度,从而按L∞(L2(Ω) 模达到最优．     

差分流线扩散法的局域稳定性分析

本文讨论差分流线扩散法的局部稳定性分析，在理论上证明了该方法依旧保持着流线扩散法扰动局部影响的特性。