Study on the most suitable computational method for diffusion numerical simulation

最适合扩散数值模拟的计算方法研究

基本信息

批准号：
06555150
负责人：
KOMATSU Toshimitsu
金额：
$ 2.62万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Developmental Scientific Research (B)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

1. Taking into account the highly accurate and stable features of the finite difference of second order derivative, the new refined scheme for advection is developed based on the concept of solving 2nd order wave equation instead of 1st order advection equation. Characteristics method is used in order to get an accurate solution propagating downstream only. From Taylor series analysis and many numerical experiments, parameters involved in this method could be determined as functions of Courant number. Comparison of this scheme with the other various ones in model calculations and Von Neumann stability analysis prove its superior accuracy and stability. This scheme can easily be applied to multidimensional practical problems by separating characteristic curve each component direction. This proposed scheme uses only three computational grid points, so that there is no need to pay much attention to the treatment at the boundary.2. On making accurately and effectively a numerical diffusion simulation, one should pay much attention to both the computational scheme for calculating the advection term and the computational grid size. The usable schemes for obtaining the high-accurate results depend on not only computational conditions such as grid intervals on time and space but also hydraulic conditions such as physical diffusion and velocity, while there will be the most effective grid size to get accurate solution within the allowable margin of error if the scheme used for the numerical simulation is chosen. We have attempted to develop a criterion for selecting the most usable scheme to calculate the advection term and deciding the most effective computational grid size. We made a 2nd order numerical diffusion term represent the truncation error terms, which is a infinite series. The criterion was made up by utilizing the 2nd order numerical diffusivity. Some one-dimensional test diffusion simulations have been carried out to inspect the validity of the criterion

1.考虑到二阶导数有限差分高精度和稳定的特点，基于求解二阶波动方程代替一阶平流方程的概念，提出了新的平流细化方案。使用特征方法是为了获得仅向下游传播的准确解。根据泰勒级数分析和大量数值实验，该方法涉及的参数可以确定为库朗数的函数。该方案与其他各种方案在模型计算和冯·诺依曼稳定性分析方面的比较证明了其优越的精度和稳定性。通过分离特征曲线各分量方向，该方案可以很容易地应用于多维实际问题。该方案仅使用三个计算网格点，因此无需过多关注边界处的处理。 2．准确有效地进行数值扩散模拟，既要重视平流项的计算方案，又要重视计算网格的大小。获得高精度结果的可用方案不仅取决于时间和空间上的网格间隔等计算条件，还取决于物理扩散和速度等水力条件，而在有限的范围内将存在获得精确解的最有效的网格尺寸。如果选择用于数值模拟的方案，则允许误差范围。我们试图制定一个标准来选择最可用的方案来计算平流项并确定最有效的计算网格大小。我们用二阶数值扩散项来表示截断误差项，它是一个无穷级数。该标准是利用二阶数值扩散率制定的。进行了一些一维测试扩散模拟来检验准则的有效性