Central schemes are frequently used for incompressible and compressible flowcalculations. The present paper is the first in a forthcoming series where anew approach to a 2nd order accurate Finite Volume scheme operating oncartesian grids is discussed. Here we start with an adaptively refinedcartesian primal grid in 3D and present a construction technique for thestaggered dual grid based on $L^{\infty}$-Voronoi cells. The local refinementconstellation on the primal grid leads to a finite number of uniquely definedlocal patterns on a primal cell. Assembling adjacent local patterns forms thedual grid. All local patterns can be analysed in advance. Later, running thenumerical scheme on staggered grids, all necessary geometric information caninstantly be retrieved from lookup-tables. The new scheme is compared toestablished ones in terms of algorithmical complexity and computational effort.
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机译：中央方案通常用于不可压缩和可压缩流量计算。本文是即将发布的系列文章中的第一篇，其中讨论了在笛卡尔网格上操作二阶精确有限体积方案的新方法。在这里，我们从3D的自适应精制笛卡尔原始网格开始，并提出一种基于$ L ^ {\ infty} $-Voronoi细胞的交错双网格的构建技术。在原始网格上的局部细化星座导致在原始单元上有限数量的唯一定义的局部模式。组装相邻的局部图案形成双网格。可以预先分析所有局部模式。稍后，在交错网格上运行数字方案，可以从查找表中即时检索所有必要的几何信息。在算法复杂度和计算量方面，将新方案与已建立的方案进行了比较。
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