网格Peclet数和网格尺寸对对流扩散方程差分格式精度的影响

用泰勒级数展开法对对流扩散方程中的扩散项进行了理论分析，从而证明对于给定的差分格式，不仅网格Ｐｅｃｌｅｔ数不能任意选取，而且网格尺寸也不能随意设定。用四种格式对一维有源对流扩散方程进行了计算，结果表明网格尺寸对差分格式精度的影响比网格Ｐｅｃｌｅｔ数更明显。为了得到真实可靠的结果，所用差分格式的阶数愈高，相应的网格尺寸就必须愈小。二阶以上的高精度迎风差分格式与二阶迎风格式相比，并无明显的优势，建议一般不必要采用二阶以上的高精度差分格式。

基于对流与扩散效应的非正交曲线网格生成及三维潮流数值模拟

非正交曲线网格具有类似非结构网格的灵活性,同时,基于非正交曲线网格的三维数学模型又具备高效、无条件稳定的优势。本文借鉴Cauchy-Riemann条件,引入表征对流强度与扩散强度之比的Peclet数,构造了生成非正交曲线网格的调节因子,将曲线网格与动力环境紧密联系。对调节因子的收敛性分析表明,实际问题中非正交曲线网格生成的收敛性可以保证。由此,利用长江口水下地形生成了具有多级分汊、多联通特点的非正交曲线网格,并就长江口的三维潮流场进行模拟。结果表明,基于Peclet数生成的非正交曲线网格在复杂河口的三维潮流数值模拟中适用性良好,且有利于局部复杂流态的模拟。

Stability-Controllable Second-Order DifferenceScheme for Convection Term

A new finite difference scheme-SCSD scheme has been proposed based on CD (Central Difference)scheme and SUD (Secondr-order Upwind Difference) scheme. Its basic feature is controIlable convectivesfability and always second-order accuracy (Stability-Controllable Second-order Difference ). It hasbeen proven that this scheme is convective-stable if the grid Peclet number .The advanage of this new scheme has been discussed based on the modified wavenumber analysis byusing Fourier transform. This scheme has been applied to the 2-D incompressible convective-diffusiveequation and 2-D compressible Euler equation, and corresponding finite difference equations have beenderived. Numerical examples of 1-D Burgers equation and 2-D transport equation have been presentedto show its good accuracy and controllable convective