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Multiscale analysis and numerical simulation for stability of the incompressible flow of a Maxwell fluid

机译：麦克斯韦流体不可压缩流稳定性的多尺度分析和数值模拟

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摘要

How to predict the stability of a small-scale flow subject to perturbations is a significant multiscale problem. It is difficult to directly study the stability by the theoretical analysis for the incompressible flow of a Maxwell fluid because of its analytical complexity. Here, we develop the multiscale analysis method based on the mathematical homogenization theory in the stress-stream function formulation. This method is used to derive the homogenized equation which governs the transport of the large-scale perturbations. The linear stabilities of the large-scale perturbations are analyzed theoretically based on the linearized homogenized equation, while the effect of the nonlinear terms on the linear stability results is discussed numerically based on the nonlinear homogenized equation. The agreements between the multiscale predictions and the direct numerical simulations demonstrate the multiscale analysis method is effective and credible to predict stabilities of flows.
机译：如何预测受到扰动的小尺度流动的稳定性是一个重大的多尺度问题。由于麦克斯韦流体不可压缩流的分析复杂性，很难通过理论分析直接研究其稳定性。在这里，我们在应力-流函数公式中基于数学均化理论开发了多尺度分析方法。该方法用于推导控制大型扰动传输的均化方程。在线性均化方程的基础上，对大型扰动的线性稳定性进行了理论分析，而在非线性均化方程的基础上，从数值上讨论了非线性项对线性稳定性结果的影响。多尺度预测与直接数值模拟之间的一致性表明，多尺度分析方法可有效且可靠地预测流动的稳定性。

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