A small amount of polymer additives can cause substantial reduction in the energy dissipation and friction loss of turbulent flow. The problem of polymer-induced drag reduction has attracted continuous attention over the seven decades since its discovery. However, changes in research paradigm and perspectives have triggered a wave of new advancements in the past decade. This review attempts to bring researchers of all levels, from beginners to experts, to the forefront of this area. It starts with a comprehensive coverage of fundamental knowledge and classical findings and theories. It then highlights several recent developments that bring fresh insights into long-standing problems. Open questions and ongoing debates are also discussed.

Polymer-induced drag reduction is bounded by an asymptotic limit of maximum drag reduction (MDR). For decades, researchers have presumed that MDR reflects the convergence to an ultimate flow state that is not further changed by polymers. Our simulation shows that, as drag reduction converges to its invariant limit, the underlying dynamics continues to evolve with no sign of convergence. The stage of asymptotic drag reduction is not represented by any single flow state, but encompasses states with varying dynamical patterns, all of which are partially sustained by polymer elasticity.

Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage ($G\prime$ ) and loss moduli ($G″$ ) over a wide frequency range from a bead-spring chain model in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green−Kubo relation with a multi-tau correlator method for noise filtering generates smooth stress relaxation modulus profiles from which accurate $G\prime$ and $G″$ can be obtained. For unentangled chains, combining the Rouse model with a short-time correction provides a convenient option that circumvents the stress fluctuation challenge altogether. For non-equilibrium MD (NEMD), we found that combining a stress pre-averaging treatment with discrete Fourier transform analysis reliably computes $G\prime$ and $G″$ with a much shorter simulation length than previously reported. Comparing the efficiency and statistical accuracy of these methods, we concluded that EMD is both reliable and efficient, and is suitable when the whole spectrum of linear viscoelastic properties is desired, whereas NEMD offers flexibility only when some frequency ranges are of interest.