结合自适应网格的基于特征线方程的分离算法

A NEW GRID ADAPTIVE STRATEGY COMBINED CHARACTERIZED BASED SPLIT METHOD

提出一种新的网格自适应方法:在需要加密的网格单元中心加入新结点,并对加密后的相邻三角形网格单元进行公共边变换,构成新的网格单元.与传统的在网格边界中点加入新节点的自适应方法相比,新方法可以更加灵活地控制网格密度,加密后的网格继承原先的网格质量不发生畸变,并且算法编程简便,容易实现.将自适应网格生成方法和基于特征线方程的分离算法相结合,对空腔内不可压缩黏性流动进行了计算.在特征线方向上进行时间步离散,动量方程求解过程中采用非增量型分离算法.计算中,把求解变量梯度值作为判定准则,在变化剧烈的区域进行网格局部加密.计算结果表明该组合算法有很好的计算精度,并有效减少了计算时间和存储量.

A new self-adapting grid method is presented by adding the new point at the centre of the grid cell. Compared with the traditional method adding the new point at the median, the new refine method is more convenient to program and has better geometrical feature. At last, this paper combines the new refined method with characterized based split method to solve N-S equation. The convective acceleration term disappear along the characteristic. In order to avoid the restriction on the nature of the interpolation function, the momentum equation is solved by non-incremental split method, which satisfies the Babuska-Brezzi（BB） condition. The variable gradient is used as the adaptive parameter. The result shows the combined method has good precision and convergence.