Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of artificial diffusion (AD) for numerical stability in hyperbolic problems, which alters the physical nature of the system. This study presents a hybrid numerical procedure that integrates an upwind total variation diminishing (TVD) finite-difference scheme, which is known for its stability in hyperbolic problems, for the polymer stress convection term into an overall pseudo-spectral numerical framework. Numerically stable solutions are obtained for Weissenberg number well beyond $\mathcal{O}\left(100\right)$ without the need for either global or local AD. Side-by-side comparison with an existing pseudo-spectral code reveals the impact of AD, which is shown to differ drastically between flow regimes. Elastoinertial turbulence (EIT) becomes unphysically suppressed when AD, at any level necessary for stabilizing the pseudo-spectral method, is used. This is attributed to the importance of sharp stress shocks in its self-sustaining cycles. Nevertheless, in regimes dominated by the classical inertial mechanism for turbulence generation, there is still an acceptable range of AD that can be safely used to predict the statistics, dynamics, and structures of drag-reduced turbulence. Detailed numerical resolution analysis of the new hybrid method, especially for capturing the EIT states, is also presented.

由于粘弹性本构方程的双曲性质，对粘弹性流动进行数值模拟具有挑战性。尽管伪光谱方法具有出色的准确性和效率，但仍需要引入人工扩散（AD）来实现双曲问题中的数值稳定性，从而改变了系统的物理性质。这项研究提出了一种混合数值程序，该程序将迎风总变化量递减（TVD）有限差分方案（以其在双曲线问题中的稳定性而闻名），将聚合物应力对流项整合到整个伪谱数值框架中。Weissenberg数的数值稳定解远超过$\mathcal{Ø}（100）$无需全局或本地AD。与现有的伪频谱代码并排比较显示了AD的影响，这在流态之间表现出极大的差异。当使用稳定伪光谱方法所需的任何水平的AD时，弹性地湍流（EIT）都会受到物理上的抑制。这归因于剧烈的应力冲击在其自持周期中的重要性。然而，在由经典惯性机理产生湍流的状态下，仍然存在可接受的AD范围，该范围可以安全地用于预测减阻湍流的统计量，动力学和结构。还介绍了新混合方法的详细数值分辨率分析，尤其是用于捕获EIT状态的数值分辨率分析。