Monotonicity-Preserving激波捕捉格式在湍流大尺度模拟中的评估

对高阶激波捕捉格式的性能进行了系统的测评,重点分析了Suresh和Huynh(1997)所提出的Monotonicity-Preserving格式的性能.结果表明Monotonicity-Preserving格式的性能显著优于原始WENO(Weighted Essentially Non-Oscillatory) 格式,和改进型WENO格式相当.对格式的分析进一步表明,迎风型的激波捕捉格式在湍流模拟方面的性能都不及高阶中心格式,其原因归结为激波捕捉格式所包含的线性和非线性耗散.因此,改进高阶激波捕捉格式的关键在于同时降低格式的线性耗散和非线性耗散,以提高格式对湍流脉动能量的保持和对小尺度脉动结构的捕捉能力.

Assessment of monotonicity-preserving scheme for large-scale simulation of turbulence

The high-order shock-capturing schemes were assessed by comparing the Monotonicity-Preserving scheme proposed by Suresh and Huynh (1997) with the weighted essentially non-oscillatory schemes(WENO). Great emphasis was imposed on the analysis of the performances of Monotonicity-Preserving scheme for turbulence simulation. The assessment indicates the Monotonicity-Preserving functions much better than the original weighted essentially non-oscillatory scheme, even close to the improved weighted essentially non-oscillatory scheme. In accordance with the analysis, all the assessed shock-capturing schemes can hardly emulate the high-order central scheme in simulating isotropic turbulence, which is attributed to the linear as well as nonlinear dissipation of the shock-capturing schemes. Therefore, both the linear and nonlinear dissipation should be reduced in order to improve the high-order shock-capturing schemes in preserving turbulence energy and capturing small-scale turbulence structures.