A class of explicit forward time-difference square conservative schemes

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications. Partly supported by the State Major Key Project for Basic Researches of China Worked as a post doctor in Computing Center, Chinese Academy of Sciences, when this paper was submitted     

一种新的区域分离法

本文在特征方向法的基础上建立了一种新的区域分离法,它适于在全球或半球区域的正压“浅水”模式上实现。该方法有三个优点：第一,在分离区域的交界处的边条件不需要专门处理,可以自然吻合,这是其他区域分离法所难以达到的;第二,该方法利用地球经向为自然周期边界的特点,可以将时间步长在极区附近增大数倍,从而节省大量计算时间;第三,该方法虽然有两个分裂区域,但主体计算仍在整个大区域内进行,只是计算结果的具体处理不同而已,这样的计算十分灵活方便。     

The Lie-group shooting method for multiple-solutions of Falkner-Skan equation under suction-injection conditions

For the Falkner-Skan equation, including the Blasius equation as a special case, we develop a new numerical technique, transforming the governing equation into a non-linear second-order boundary value problem by a new transformation technique, and then solve it by the Lie-group shooting method. The second-order ordinary differential equation is singular, which is, however, much saving computational cost than the original third-order equation defined in a semi-infinite range. In order to overcome the singularity we consider a perturbed equation. The newly developed Lie-group shooting method allows us to search a missing initial slope at the left-end in a compact space of t∈[0,1], and moreover, the initial slope can be expressed as a closed-form function of r∈(0,1), where the best r is determined by matching the right-end boundary condition. All that makes the new method much superior than the conventional shooting method used in the boundary layer equation under imposed boundary conditions. When the initial slope is available we can apply the fourth-order Runge-Kutta method to calculate the solution, which is highly accurate. The present method is very effective for searching the multiple-solutions under very complex boundary conditions of suction or injection, and also allowing the motion of plate.     

A－HIGH－ORDER ACCURACY EXPLICIT DIFFERENCE SCHEME FOR SOLVING THE EQUATION OF TWO－DIMENSIONAL PARABOLIC TYPE

Ａ－ＨＩＧＨ－ＯＲＤＥＲＡＣＣＵＲＡＣＹＥＸＰＬＩＣＩＴＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＦＯＲＳＯＬＶＩＮＧＴＨＥＥＱＵＡＴＩＯＮＯＦＴＷＯ－ＤＩＭＥＮＳＩＯＮＡＬＰＡＲＡＢＯＬＩＣＴＹＰＥＭａＭｉｎｇｓｈｕ（马明书）（ＲｅｃｅｉｖｅｄＪｕｎｅ２,１...     

单点子域积分与差分

通过稳定性分析、显式与隐式积分,表明了单点子域积分相对于差分法的优越性．     

单点子域积分与差分

通过稳定性分析、显式与隐式积分，表明了单点子域积分相对于差分法的优越性．     

污染扩散方程高精度紧致格式及其稳定性分析

针对污染扩散方程提出了时间任意阶精度的显式格式,并对该格式的稳定性和精度进行了分析,理论结果表明:一阶精度的计算格式是传统的显格式,其稳定条件为:s≤1/2(s=D.Δt/Δx2,D为扩散系数,Δt为时间步长,Δx为空间步长),随着保留精度阶数的增加,稳定性范围也会随之增大;当保留无穷阶精度时,格式是无条件稳定的。这也就从一个侧面揭示了稳定性与时间精度之间的关系,为高性能数值计算格式的构思提供了可以借鉴的原则。数值算例的结果表明,本文格式具有一定的实用性。     

色散方程的高稳定性两层四点显格式的单点精细积分法

基于单点精细积分的思想,对色散方程Ut=aUxxx构造了一类高稳定性的两层四点显式差分格式,其局部截断误差为O(τ+h),稳定性条件为|R|=|aτ/h3|≤f(β),其中f(β)对任意正实数β为单调递增函数.它们不仅显著地改善了同类格式的稳定性条件|R|≤0.25,而且也优于众多三层多点(5点或5点以上)显格式的稳定性条件.     

The Lie-group shooting method for boundary-layer problems with suction/injection/reverse flow conditions for power-law fluids

For power-law fluids we propose a Lie-group shooting method to tackle the boundary-layer problems under a suction/injection as well as a reverse flow boundary conditions. The Crocco transformation is employed to reduce the third-order equation to a second-order ordinary differential equation, and then through a symmetric extension to a boundary value problem with constant boundary conditions, which can be solved numerically by the Lie-group shooting method. However, the resulting equation is singular, which might be difficult to solve, and we propose a technique to overcome the initial impulse caused by the singularity using a very small time-step integration at the first few time steps. Because we can express the missing initial condition through a closed-form formula in terms of the weighting factor r∈(0,1), the Lie-group shooting method is very effective for searching the multiple-solutions of a reverse flow boundary condition.     

一种高效的局部径向基点插值无网格方法

提出了一种弹性动力分析的高效局部径向基点插值无网格方法(MLRPI).该方法采用径向基点插值形函数近似解变量,运用局部Petrov-Galerkin法推导出了相应的离散方程,并根据波动模拟的精度要求,得到某一结点的动力方程.然后采用Newmark常平均加速度法和中心差分法相结合的显式积分格式进行时域积分,得到每个自由度的一种解耦递推格式.最后,对一平面应变问题进行了求解,比较了该文提出的解耦MI.RPI方法、常规MLRPI方法和ANSYS有限元方法的精度和计算时间,结果表明解耦MLRPI方法与常规MLRPI方法的精度相当,但计算效率大大提高.     

色散方程的高稳定性三层五点显格式的广义单点精细积分法

基于文[1]中的单点精细积分方法,对色散方程Ut=aUxxx提出了一种构造高稳定性三层五点(蛙跳)显格式的广义单点精细积分法.文中格式的局部截断误差为O(τ2+h2),而稳定性条件为|R|≤g(β)(其中g对任意正实数是单调递增函数),是同类格式中最好的[2].