为了减小TVD格式的数值粘性,提高TVD格式的分辨度,提出了一种具有较小数值耗散的Harten型TVD格式.数值模拟结果表明,这种Harten型TVD格式比原来的Harten格式^[1]及其改进形式Harten-Yee^[2]的TVD格式能更好地模拟出边界层及涡流.

本文从Sweby的显式TVD格式^[2,3]出发,构造发一个推进方向一阶精度、侧向二阶精度的隐式TVD差分格式,并用于解可压缩流定常简化Naviev-Stokes(SNS)方程。对不出现流向分离的平板边界层和激波—边界层相互干扰两个问题的数值计算表明,方法可以有效捕捉流场中的间断。

This paper presents some preliminary work on the application of Schwarz alternating method, combined with a multigrid solver, for solving the steady 2D viscous incompressible Navier-Stokes equations. The difficulty caused by the violation of the compatibility condition imposed on the normal velocity at the boundary, which arises when subdomain problems are not solved exactly at each iteration, is surrounded by adding artificial compressiblity constants to the continuity equation each time when a subdomain problem is to be solved. These constants permit to maintain the compatibility condition of the subdomain problems and one can easily show that they tend to zero when the iteration number tends to infinity (in fact, they can be expressed explicitly as functions of the iteration number and some geometrical parameters of the computational domain). Numerical experiences have been made for flows in a channel with a facing step.

本文首先从单个方程出发,根据TVD思想,比较自然地给出了二阶带通量限制器的CSCM^[1]差分方法,然后推广到方程组情形。为了验证方法和程序,将球头绕流计算结果同文献[2]作了比较,然后运用此方法模拟了轴对称凹型钝体的粘性超音速分离绕流流场,对一阶与二阶、粘性与无粘性数值结果作了比较。计算网格采用了简单、快速易行的拟正交代数生成方法。