非结构有限体积耗散格式精度分析

Accuracy Analysis of Unstructured Finite Volume Discretization Scheme for Diffusive Flux

针对耗散方程非结构网格有限体积离散,基于一维非均匀网格构造了包含相容项和高频阻尼项的耗散格式,结合模型方程研究了耗散格式的相容性条件及高频阻尼系数最优值与梯度格式的关联关系;耗散格式严格满足截断误差相容性的条件是相容项采用代数平均加权且高频阻尼系数为1;在均匀网格条件下,可实现耗散格式最高离散精度的高频阻尼系数最优值取决于梯度格式的2阶截断误差系数;根据梯度格式的不同,高频阻尼系数最优值的取值范围在1与2之间;在非均匀网格条件下,不同梯度格式对耗散格式相容性及离散精度均有显著的影响,采用均匀网格条件下的高频阻尼系数最优值可得到更小的离散误差。

For finite volume discretization of diffusive equation on unstructured mesh,the diffusive flux scheme consists of consistent term and high-frequency damping term was constructed based on non-uniform one-dimension mesh.The diffusive model was conducted to investigate the consistency condition for general mesh and the relationship between optimized coefficient of high-frequency damping and gradient scheme.Results show that arithmetical averaged consistent term with high-frequency damping coefficient of1is necessary for the diffusive scheme to be consistent on general mesh.For uniform grid,the optimized value of high frequency damping coefficient,which leads to the best accuracy of diffusive flux,depends on the coefficient of second order truncation error of the gradient scheme.The optimized value of high frequency damping coefficient is between1and2,according to different gradient schemes.For non-uniform mesh,gradient scheme has significant influence on consistency and accuracy of diffusive scheme.The optimized value of high frequency damping coefficient for uniform mesh can decrease the discretization error effectively on non-uniform mesh.