线性Schrdinger方程的两个时间分裂差分格式

针对物理问题中常常需要求解一类线性Schrdinger方程的问题,本文中提出两个构造简单、精度高、便于计算的时间分裂差分格式.用方程的平面波解证明两个格式的精度都为O(τ2+h2),并用线性化的分析方法证明两个格式的稳定性和收敛性.数值实验表明,在计算量较大的情况下,要保证相当的精度,提出的两个格式可以有效地节省计算时间.

求解二维 Navier-Stokes 方程的谱元法

研究了谱元法的插值函数选取和谱元法的离散，给出离散方程的一般形式，分析了误差和收敛速度，并采用时间分裂格式的谱元法求解ＮａｖｉｅｒＳｔｏｋｅｓ方程，计算表明结果是令人满意的，方法不仅具有良好的稳定性而且具有较高的精度，易于推广到三维及湍流的直接数值模拟中去。

求解二维Navier-Stokes方程的谱元法

本文研究了谱元法的插值函数选取和谱元法的离散,给出离散方程的一般形式,分析了误差和收敛速度,并采用时间分裂格式的谱元法求解Navier-Stokes方程,计算表明结果是令人满意的,方法不仅具有良好的稳定性而且具有较高的精度,易于推广到三维及湍流的直接数值模拟中去。

NUMERICAL SIMULATIONS OF EVOLUTIONS FROM WALL PULSE TO TURBULENT COHE RENT STRUCTURES

The high order compact d if ference method is developed for solving the perturbation equations based on Navi er Stokes equations, and is used in studying complex evolution processes from w all negative pulse to the turbulent coherent structure in the channel flow. Th is method contains three dimensional coupling difference scheme with high accur acy and high resolution, and the high order time splitting methods. Compared with the general spectral method, the method can be used to research turbule nt coherent structure under more general boundary conditions and in flow domains . In this paper, the generation and evolution of the turbulent coherent structur es ind uced by wall pulse in the channel flow are simulated, and the basic characterist ics and rules of the turbulent coherent structure are shown. Computational r esults indicate that a wall negative pulse is more convenient than the resonant three wave model.