A new spectrally optimized physical dispersion relation preserving scheme has been introduced to solve computational acoustics and aeroacoustics problems, accurately. The derived fourth-order accurate scheme has significant spectral resolution and physical dispersion relation preserving (DRP) nature. The scheme displays neutral stability at high CFL numbers. The developed scheme has an ability to add numerical diffusion as and when required to attenuate spurious waves present in the computed solutions. These features make the proposed scheme suitable for solving computational aeroacoustic problems. The scheme has been validated by comparing solutions of model computational acoustic problems with the available analytical solutions. Scheme has also been tested to solve the incompressible flow field around a circular cylinder executing rotary oscillations. Ability of the scheme to perform direct simulation of the computational aeroacoustic problems has been shown by computing acoustic field triggered by a laminar flow past a stationary circular cylinder. Excellent match has been observed between the present computed results and the available results in the literature which justifies applicability of the present DRP scheme to solve complex flow and aeroacoustic problems.

中文翻译：

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使用新的弥散关系保留方案计算气动声学和流体流动问题

引入了一种新的光谱优化物理色散关系保持方案，以准确地解决计算声学和气动声学问题。导出的四阶精确方案具有显着的光谱分辨率和物理色散关系保持 (DRP) 特性。该方案在高 CFL 数下显示中性稳定性。开发的方案能够在需要时添加数值扩散，以衰减计算解决方案中存在的杂散波。这些特征使得所提出的方案适用于解决计算气动声学问题。该方案已通过将模型计算声学问题的解决方案与可用的分析解决方案进行比较来验证。方案也已经过测试，以解决执行旋转振荡的圆柱体周围的不可压缩流场。通过计算由流过静止圆柱体的层流触发的声场，该方案能够直接模拟计算气动声学问题。在目前的计算结果和文献中的可用结果之间观察到了很好的匹配，这证明了目前的 DRP 方案在解决复杂的流动和气动声学问题方面的适用性。