论文标题
在可压缩流量的模拟中，全球和局部质量，动量和动能的保护
Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flow
论文作者
论文摘要
从抽象的角度研究了可压缩流程方程中对流术语的空间离散化，以获取有限差分方法和带有细胞中心数值通量的有限量 - 体积类型。寻求一般条件，以登机网格的本地和全球守恒对原发性（质量和动量）以及次级（动能）不变性。基于矩阵方法的分析表明，可以获得全球和局部保护的尖锐标准，并且在许多情况下，这两个概念是等效的。显式数值通量是在保证全球保护的所有有限差分公式中得出的，即使对于不均匀的笛卡尔网格。该处理还揭示了保守的有限差异配方与以细胞为中心的有限体积类型方法之间的紧密关系。这个类比表明，在本地保存原发性和次要不变性的一类有限差异化离散剂的设计。
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions are sought for the local and global conservation of primary (mass and momentum) and secondary (kinetic energy) invariants on Cartesian meshes. The analysis, based on a matrix approach, shows that sharp criteria for global and local conservation can be obtained and that in many cases these two concepts are equivalent. Explicit numerical fluxes are derived in all finite-difference formulations for which global conservation is guaranteed, even for non-uniform Cartesian meshes. The treatment reveals also an intimate relation between conservative finite-difference formulations and cell-centered finite-volume type approaches. This analogy suggests the design of wider classes of finite-difference discretizations locally preserving primary and secondary invariants.
