求解不可压流动近似投影方法的精度分析  

Accuracy analysis of approximate projection methods for solving incompressible flows

作　　者：王跃[1] 任玉新[1] 

机构地区：[1]清华大学航天航空学院,北京100084

出　　处：《清华大学学报（自然科学版）》2008年第2期280-284,共5页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(10572075)

摘　　要：在非交错网格上开发具有高精度、高效率的投影方法,对于数值求解不可压流动具有重要意义。非交错网格上经过Armfield修正的近似投影方法可以有效抑制压力场的数值振荡,但它在离散的连续方程中引入了和压力四阶导数有关的人工源项。该文通过理论分析指出这个人工源项会使该方法的时间精度降到一阶。考察了一个双周期剪切层流动的算例,通过与交错网格上的投影方法、非交错网格上经压力光滑的精确投影方法对比,说明了这个人工源项是导致该方法时间精度降低的原因。Developing projection method on non staggered grids with high accuracy and high efficiency is important for numerical simulation of incompressible flows, The approximate projection method with the Armfield correction on non-staggered grids can effectively suppress numerical oscillations in the pressure field. however, it introduces an artificial source term related to the fourth order derivative of pressure into the discrete continuity equation, By theoretical analysis, we show that this artificial source term reduces the time accuracy of the method to first order, The time accuracy of the method for a double periodic shear layer is compared with that of projection method on staggered grids and exact projection method with a pressure smoother on non staggered grids, verifying that the artificial source term is responsible for the time accuracy decrease.

关 键 词：不可压流动 近似投影方法 Armfield修正 时间精度 

分 类 号：O351.3[理学—流体力学]