高分辨率共轭滤波器用于流动模拟
High resolution conjugate filters for the simulation of flows
AI总结：
本文提出基于Hermite核的CFOR方案，利用DSC算法生成共轭高低通滤波器，实现流动模拟中高分辨率与振荡抑制，并通过数值实验验证其优越性。
摘要：
本文提出了一种用于流体流动模拟的共轭滤波器振荡抑制（CFOR）方案的Hermite核实现。该Hermite核通过使用离散奇异卷积（DSC）算法构造，该算法系统地生成了低通滤波器及其共轭高通滤波器。高通滤波器用于近似求解流动方程中的空间导数，而共轭低通滤波器则被激活以消除流动时间演化过程中累积的伪振荡。由于低通和高通滤波器均源自Hermite核，它们具有相似的正则性、时频局部化、有效频带和紧支撑性。傅里叶分析表明，CFOR-Hermite方案产生了近乎最优的分辨率，并且比先前的CFOR方案更接近理想低通滤波器的近似。因此，它在分辨激波产生的自然高频振荡方面具有更好的潜力。本文采用大量一维和二维数值算例，包括可压缩和不可压缩流动，以及有激波和无激波的情况，以探索该CFOR-Hermite方案的实用性、测试其分辨率并检验其稳定性。在求解Taylor问题、推进波包以及分辨激波/熵波相互作用时，实现了极小的每波长点数（PPW）比值。本文对等熵涡对流的结果与文献中的结果相比非常有利。
英文摘要：
This paper proposes a Hermite-kernel realization of the conjugate filter oscillation reduction (CFOR) scheme for the simulation of fluid flows. The Hermite kernel is constructed by using the discrete singular convolution (DSC) algorithm, which provides a systematic generation of low-pass filter and its conjugate high-pass filters. The high-pass filters are utilized for approximating spatial derivatives in solving flow equations, while the conjugate low-pass filter is activated to eliminate spurious oscillations accumulated during the time evolution of a flow. As both low-pass and high-pass filters are derived from the Hermite kernel, they have similar regularity, time-frequency localization, effective frequency band and compact support. Fourier analysis indicates that the CFOR-Hermite scheme yields a nearly optimal resolution and has a better approximation to the ideal low-pass filter than previously CFOR schemes. Thus, it has better potential for resolving natural high frequency oscillations from a shock. Extensive one- and two-dimensional numerical examples, including both incompressible and compressible flows, with or without shocks, are employed to explore the utility, test the resolution, and examine the stability of the present CFOR-Hermite scheme. Extremely small ratio of point-per-wavelength (PPW) is achieved in solving the Taylor problem, advancing a wavepacket and resolving a shock/entropy wave interaction. The present results for the advection of an isentropic vortex compare very favorably to those in the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
