SIMPLE算法的一种改进格式

An improved format for SIMPLE algorithm

在连续性方程中人为加入压力的时间导数项,将人工可压缩方法与压力泊松方程相结合起来,有效抑制了由于守恒变量和非守恒变量转换引起的密度波动;运用改进的非线性动量插值格式对网格界面处的速度进行离散,消除了交错网格下棋盘式的压力波动,减小了网格界面处的数值耗散限。为验证该方法的通用性,依次对方腔自然对流、顶盖驱动流和后向阶梯流进行了数值分析,证实该算法在收敛速度、稳定性方面均有较大提升。

In this paper, the artificial time derivative of pressure is added into the continuity equation, and the artificial compressibility method is combined with the pressure Poisson equation,which effectively restrains the density oscillation caused by the transformation of conservation variables and primitive variables. The improved nonlinear momentum interpolation scheme is used to discrete the velocity at the grid interface, which eliminates the pressure oscillation in the staggered grid and reduces the numerical dissipation limit at the grid interface. In order to verify the generality of this method, numerical analysis is carried out for natural convection in square cavity, case-drive flow cavity and backward step flow successively. It proves that the convergence rate and stability of this algorithm are improved greatly.