A class of high-order nonlinear filter schemes by Yee et al. (J Comput Phys 150:199–238, 1999), Sjogreen and Yee (J Comput Phys 225:910–934, 2007), and Kotov et al. (Commun Comput Phys 19:273–300, 2016; J Comput Phys 307:189–202, 2016) is examined for long-time integrations of computational aeroacoustics (CAA) turbulence applications. This class of schemes was designed for an improved nonlinear stability and accuracy for long-time integration of compressible direct numerical simulation and large eddy simulation computations for both shock-free turbulence and turbulence with shocks. They are based on the skew-symmetric splitting version of the high-order central base scheme in conjunction with adaptive low-dissipation control via a nonlinear filter step to help with stability and accuracy capturing at shock-free regions as well as in the vicinity of discontinuities. The central dispersion-relation-preserving schemes as well as classical central schemes of arbitrary orders fit into the framework of skew-symmetric splitting of the inviscid flux derivatives. Numerical experiments on CAA turbulence test cases are validated.

中文翻译：

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用于计算有冲击的气动声学湍流的具有非线性滤波器的高阶中心方案的斜对称分裂

Yee 等人的一类高阶非线性滤波器方案。(J Comput Phys 150:199–238, 1999)、Sjogreen 和 Yee (J Comput Phys 225:910–934, 2007) 和 Kotov 等人。（Commun Comput Phys 19:273–300, 2016; J Comput Phys 307:189–202, 2016）研究了计算气动声学 (CAA) 湍流应用的长期集成。此类方案旨在提高非线性稳定性和准确性，用于可压缩直接数值模拟和无冲击湍流和有冲击湍流的大涡模拟计算的长期集成。它们基于高阶中央基础方案的偏斜对称分裂版本，并结合通过非线性滤波器步长的自适应低耗散控制，以帮助在无冲击区域以及附近的稳定性和精度捕获不连续性。中心色散关系保持方案以及任意阶的经典中心方案适合无粘性通量导数的偏对称分裂框架。CAA湍流测试案例的数值实验得到验证。