论文标题
粘度系数的算术平均值足以在非结构化网格上二阶有限量粘性离散
Arithmetic Averages of Viscosity Coefficient are Sufficient for Second-Order Finite-Volume Viscous Discretization on Unstructured Grids
论文作者
论文摘要
In this short note, we discuss the use of arithmetic averages for the evaluation of viscous coefficients such as temperature and velocity components at a face as required in a cell-centered finite-volume viscous discretization on unstructured grids, and show that second-order accuracy can be achieved even when the arithmetic average is not linearly-exact second-order reconstruction at a face center (e.g., the face center在两个相邻的细胞质心之间并不完全位于非结构性网格中。与无粘性离散化不同，必须将解决方案以线性精确的方式重建到面向二阶精度，而粘性离散化不需要线性精确性来计算面部的粘性系数。二阶准确度有两个要求，算术平均值满足两个。对于一个简单的一维非线性扩散问题以及基于制造溶液的方法，用于简单的一维非线性扩散问题以及三维粘性问题，可以证明二阶精度。
In this short note, we discuss the use of arithmetic averages for the evaluation of viscous coefficients such as temperature and velocity components at a face as required in a cell-centered finite-volume viscous discretization on unstructured grids, and show that second-order accuracy can be achieved even when the arithmetic average is not linearly-exact second-order reconstruction at a face center (e.g., the face center is not located exactly halfway between two adjacent cell centroids) as typical in unstructured grids. Unlike inviscid discretizations, where the solution has to be reconstructed in a linearly exact manner to the face center for second-order accuracy, the viscous discretization does not require the linear exactness for computing viscous coefficients at a face. There are two requirements for second-order accuracy, and the arithmetic average satisfies both of them. Second-order accuracy is numerically demonstrated for a simple one-dimensional nonlinear diffusion problem and for a three-dimensional viscous problem based on methods of manufactured solutions.
