摘要
建立具有统一形式的明满交替流控制方程。由于系统阵刚性而导致明满交替流数值模拟的计算精度低和收敛性差。在交错网格上对控制方程进行空间上的数值离散后,加入伪时间导数项进行预处理,改善系统阵的刚性。通过采用系统阵增维的方法将非齐次状态空间方程转化为齐次方程,避免了矩阵求逆运算,增强计算的稳定性;预处理后系统方程每一个物理时间步的求解都相当于一个稳态问题,需要花费大量的计算时间,借助于精细积分法可以采用大步长的优势来加快求解速度。有效地解决了明满交替流建模中由于刚性而引起的数值稳定性问题和预处理引起的积分时间较慢的问题。而且这一方法具有程序容易实现的优点。
The governing equation with unified formulation is set up for mixed free-surface-pressure flow. The difficulties that arise in simulation algorithms are due to the poor conditioning of the eigenvalues of the mixed free-surface-pressure flow system. It leads to poor solution accuracy as well as poor convergency. Discretized governing equations are built up with staggered grid, and then the governing equations are preconditioned by adding virtual time term for improving the poor conditioning of the eigenvalues of the system. Non-homogeneous equations are converted into homogeneous equations by means of increment dimensional method and the numerical stability can be enhanced as the matrix inversion calculation is avoided. The implementation of the preconditioned dual-time algorithm in each physical-time step is to solve a steady flows problem and slow to converge. The precise integration method has the properties for rapidly solving the steady system for a large step can be applied. As a result, the numerical stability problem is improved by precondition algorithm for mixed free-surface-pressure flow and the poor convergence time is improved by precise integration. In addition, the programming implementation is easy.
出处
《水动力学研究与进展（A辑）》
CSCD
北大核心
2006年第4期533-537,共5页
Chinese Journal of Hydrodynamics
关键词
明满交替流
预处理
精细积分
mixed free-surface-pressure flow
precondition
precise integration
