The essence of the maximum drag reduction (MDR) state of viscoelastic drag-reducing turbulence (DRT) is still under debate, which mainly holds two different types of views: the marginal state of inertial turbulence (IT) and elasto-inertial turbulence (EIT). To further promote its understanding, this paper conducts a large number of direct numerical simulations of DRT at a modest Reynolds number Re with $Re = 6000$ for the FENE-P model that covers a wide range of flow states and focuses on the problem of how nonlinear extension affects the nature of MDR by varying the maximum extension length $L$ of polymers. It demonstrates that the essence of the MDR state can be both IT and EIT, where $L$ is somehow an important parameter in determining the dominant dynamics. Moreover, there exists a critical $L_c$ under which the minimum flow drag can be achieved in the MDR state even exceeding the suggested MDR limit. Systematic analyses on the statistical properties, energy spectrum, characteristic structures and underly dynamics show that the dominant dynamics of the MDR state gradually shift from IT-related to EIT-related dynamics with an increase of $L$ . The above effects can be explained by the effective elasticity introduced by different $L$ at a fixed Weissenberg number (Wi) as well as the excitation of pure EIT. It indicates that larger $L$ introduces more effective elasticity and is favourable to EIT excitation. Therefore, we argue that the MDR state is still dominated by IT-related dynamics for the case of small $L$ , but replaced by EIT-related dynamics at high $L$ . The obtained results can harmonize the seemingly controversial viewpoints on the dominant dynamics of the MDR state and also provide some ideas for breaking through the MDR limit, such as searching for a polymer solution with a proper molecular length and concentration.

The high Weissenberg number (Wi) problem (HWNP) has long been a challenge of high-Wi viscoelastic fluid flow simulation. This letter points out that the tensor interpolation method during solving the differential constitutive equations is the main origin of the loss of symmetric positive-definite (SPD) property of the conformation tensor which is the trigger of the HWNP. Instead of component-based interpolation, we propose a tensor-based interpolation method and the results show that this method is very effective in tackling the HWNP by guaranteeing the SPD property of the conformation tensor as well as numerical accuracy. Moreover, the high-order total variation diminishing (TVD) schemes can also be easily constructed under the proposed framework.