一种稳定性与精度协调一致的二阶差分格式  

Stability-Accuracy-Compatible Second-Order Difference Scheme

作　　者：王贤钢[1] 俞茂铮[1] 陶文铨[1] 

机构地区：[1]西安交通大学动力工程多相流国家重点实验室,西安710049

出　　处：《西安交通大学学报》2005年第11期1194-1198,共5页Journal of Xi'an Jiaotong University

摘　　要：针对保证稳定性的二阶差分(SGSD)格式在网格Peclet数较大时会与二阶迎风(SUD)格式一样引起较严重的假扩散问题,在SGSD格式的基础上,通过引入一个与最大网格Peclet数相关的参数,提出了一种可以减少假扩散的稳定性与精度协调一致的二阶差分(SACSD)格式.应用SACSD和其他4种格式计算了两个经典流动问题,结果表明:SACSD格式的精度至少不比SGSD、CD和SUD格式低,有时甚至比QUICK格式还要高,且稳定性比QUICK格式好.SACSD格式具有较高的计算精度和很好的对流稳定性,因此在进行工程流动与换热问题的数值计算时是一种很有价值的格式.The stability guaranteed second-order difference （SGSD） scheme may cause severe false diffusion just like the second-order upwind difference （SUD） scheme when the grid Peclet number is comparatively large. Based on the SGSD scheme, a new stability-accuracy-compatible second-order difference （SACSD） scheme was proposed to reduce false diffusion by introducing a parameter which is dependent on the maximum grid Peclet number. The computational results of two benchmark problems using the SACSD and other four schemes show that the numerical accuracy of the SACSD scheme is at least no less than those of the SGSD, central difference （CD） and SUD schemes, and sometimes higher than that of the QUICK scheme. The stability of the SACSD scheme is higher than that of the QUICK scheme. Because of the high efficiency and good robustness the SACSD scheme is feasible in numerical computations for fluid flow and heat transfer problems.

关 键 词：数值计算 差分格式 精度 稳定性 

分 类 号：TK124[动力工程及工程热物理—工程热物理]