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首页> 外文期刊>Journal of Computational Physics >Adjoint algorithms for the Navier-Stokes equations in the low Mach number limit
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Adjoint algorithms for the Navier-Stokes equations in the low Mach number limit

机译：马赫数下限下的Navier-Stokes方程的伴随算法

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This paper describes a derivation of the adjoint low Mach number equations and their implementation and validation within a global mode solver. The advantage of using the low Mach number equations and their adjoints is that they are appropriate for flows with variable density, such as flames, but do not require resolution of acoustic waves. Two versions of the adjoint are implemented and assessed: a discrete-adjoint and a continuous-adjoint. The most unstable global mode calculated with the discrete-adjoint has exactly the same eigenvalue as the corresponding direct global mode but contains numerical artifacts near the inlet. The most unstable global mode calculated with the continuous-adjoint has no numerical artifacts but a slightly different eigenvalue. The eigenvalues converge, however, as the timestep reduces. Apart from the numerical artifacts, the mode shapes are very similar, which supports the expectation that they are otherwise equivalent. The continuous-adjoint requires less resolution and usually converges more quickly than the discrete-adjoint but is more challenging to implement. Finally, the direct and adjoint global modes are combined in order to calculate the wavemaker region of a low density jet.
机译：本文介绍了伴随的低马赫数方程的推导及其在全局模式求解器中的实现和验证。使用低马赫数方程式及其伴随项的优点在于，它们适用于密度可变的流（例如火焰），但不需要解析声波。实施并评估了两个版本的伴随：离散伴随和连续伴随。用离散伴随计算出的最不稳定的全局模式具有与相应的直接全局模式完全相同的特征值，但是在入口附近包含数值伪像。用连续伴随算出的最不稳定的全局模式没有数值假象，但特征值略有不同。但是，随着时间步长的减小，特征值会收敛。除了数字伪像外，众数形状非常相似，这支持了它们在其他方面是等效的期望。连续伴奏需要的分辨率较低，并且通常比离散伴奏的收敛速度更快，但是实现起来更具挑战性。最后，直接和伴随的全局模式被组合以便计算低密度射流的造波器区域。

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