摘要
应用常规数值方法求解对流占优的对流扩散方程时会出现非物理的数值伪振荡现象。因此本文提出了一种基于无网格径向点插值法的自适应布点方案,并成功地解决了对流占优时的数值伪振荡问题。在自适应布点的实施过程中,该方案将无网格方法中的背景积分单元作为自适应控制的梯度计算单元,并将该控制单元场函数梯度的大小作为自适应的梯度控制指标,然后给定相应的梯度控制限,通过控制指标和梯度限的比较来指示高梯度区域进行自适应中心加点和梯度计算单元的分解。数值结果表明:这种基于无网格径向点插值法的自适应布点方案不仅能有效地消除对流占优时的数值伪振荡现象,而且它还具有计算精度高、数值稳定性好、算法实施简单、前后处理方便的优点。
It is well known that the numerical solutions of conventional methods may be corrupted by nonphysical oscillations when the convection action dominates the diffusion action in the transport problems. The adaptive distribute points technique was developed to overcome the instability issues in convection dominated problems simulated by radial point interpolation method. In the adaptive process of meshless method, the background mesh was considered as the cell to control the grads adaptively. The grads of the cell was regarded as Grads Index, and it decided whether or not to refine the cell by comparing with Grads Bounds. Two numerical examples were presented and the numerical results show that this technique is effective to solve convection dominated problems. In addition, these methods have high accuracy and good stabilization, the computational algorithms can be easily implemented, the preprocess and post process are very convenient.
出处
《力学季刊》
CSCD
北大核心
2008年第1期85-91,共7页
Chinese Quarterly of Mechanics
基金
国家自然科学基金重大项目(10590353)
陕西省自然科学基金(2005A16)
关键词
无网格方法
对流占优
自适应
meshless method
convection dominated
adaption
