基于HWCNS格式的紧致插值方法研究

在保证良好间断捕捉能力的前提下,能够达到更高的分辨率,一直是有限差分方法努力的方向。基于HWCNS格式构造思想,发展了一种高精度非线性紧致插值方法,构造了紧致七阶HWCNS格式,分析了其频谱特性,利用多个典型算例对所构造的格式性能进行了考察。结果表明,在模拟包含间断和多尺度流动结构的长时间演化问题中,本文发展的方法在计算结果精度和综合计算效率方面优于显式五阶HWCNS和七阶WENO格式,与频谱分析结论一致。

Investigation of compact interpolation based on HWCNS schemes

Finite difference methods are always advancing to obtain higher spectral resolution with robust discontinuities-capturing capabilities.Following HWCNS formation,a new high-order nonlinear compact interpolation is proposed,then the seventh-order compact HWCNS scheme is developed and its spectrum feature is presented.Several typical cases are carried to verify the performance of the new method in this paper.In terms of computational efficiency and accuracy of the numerical results,the present compact interpolation is superior to the explicit fifth-order HWCNS and seventh-order WENO schemes for simulation of flows characterized by multiple scales and long-term evolution include discontinuities,which is in accordance with the result of spectrum analysis.