高分辨率TVD格式的改进及应用

IMPROVEMENT AND APPLICATION OF HIGH RESOLUTION TVD SCHEMES

详细分析对比了已有的Harten TVD格式在三维任意曲线坐标系下的形式,尤其是其校正流量的构造。通过几何意义及物理意义的分析,指出了其缺陷,即校正流量中包含不必要的几何参数。由此,对校正流量的构造进行了几何改进,使其满足几何与物理要求。这一改进简单、意义明确、而且不增加计算量与存储量,在网格变化剧烈处可以明显改善计算的精度。同时,也考虑了预处理下的Harten TVD格式的几何修正,并通过计算证明了在预处理修正下几何改进仍然有效。

The existed forms of Harten TVD scheme in three dimension curvilinear coordinates especially the designs of corrected flux were analyzed. Through the insight of geometrical and physical essence of scheme, the deficiency of design, that was the unwanted geometrical factor in corrected flux, was pointed out. Then, the modified method in view of geometry was applied to the design of corrected flux in order to satisfy the need of geometry and physics. The modification could improve the accuracy when grid was irregularly and uneven with the advantage of simple and clear without increasing cost of computation and memory. The modified method was also applied to the preconditioned Harten TVD scheme. The computational result indicated that the modified method was also effective with preconditioning.