M-Matrix Flux Splitting for General Full Tensor Discretization Operators on Structured and Unstructured Grids
M-Matrix Flux Splitting for General Full Tensor Discretization Operators on Structured and Unstructured Grids
复制标题
结构化和非结构化网格上通用全张量离散化算子的 M 矩阵通量分裂
DOI：
10.1006/jcph.2000.6418
复制
发表时间：
2000
影响因子：
4.1
通讯作者：
M. Edwards
中科院分区：
文献类型：
--
作者：
M. Edwards
对角张量通量近似是流体动力学中常用的一种近似方法。当坐标系与张量的主轴不对齐时，这种近似在通量中引入了O(1)误差，这在采用曲线网格时尤其常见。一般来说，一致的全张量通量近似导致支持和随之的雅可比矩阵的大小显著增加。将一般全张量通量与交叉项一起分解为对角张量通量后，在一般有限体积形式中引入时分裂半隐式、稳定的全张量通量近似，使标准对角张量雅比矩阵结构在单相流、IMPES和标准块完全隐式公式中得以保留，同时确保了结构化和非结构化网格离散化的空间一致性。证明了该方案在常椭圆系数下的稳定性。结果表明，该方法在完全隐式框架内对结构网格和非结构网格的多相流具有优越性。
Diagonal tensor flux approximations are commonly used in fluid dynamics. This approximation introduces an O(1) error in flux whenever the coordinate system is nonaligned with the principal axes of the tensor which is particularly common when employing curvilinear gridding. In general a consistent full tensor flux approximation leads to a significant increase in support and consequent size of the Jacobian matrix. After decomposition of a general full tensor flux into a diagonal tensor flux together with cross terms, time-split semi-implicit, stable, full tensor flux approximations are introduced with in a general finite volume formalism, enabling the standard diagonal tensor Jacobian matrix structure to be retained for single phase flow, IMPES, and standard block fully implicit formulations while ensuring spatial consistency of the discretization for both structured and unstructured grids. Stability of the scheme is proven for constant elliptic coefficients. The results presented demonstrate the benefits of the method for multiphase flow within a fully implicit framework on structured and unstructured grids.