We present a new approach – the entropy-viscosity method (EVM) – for numerical modelling of high Reynolds number flows and investigate its potential by simulating fully developed incompressible turbulent flow, first in a stationary pipe and subsequently in a flexible pipe. This method, which was first proposed by Guermond et al. (J. Comput. Phys., vol. 230 (11), 2011, pp. 4248–4267), introduces the concept of entropy viscosity, computed based on the nonlinear localized residual obtained from the energy equation. Specifically, this nonlinear viscosity based on the local size of entropy production is added to the spectral element discretization employed in our work for stabilization at insufficient resolution. Unlike its original formulation, which includes an ad hoc tuneable parameter . Both pressure and velocity correlations exhibit cellular patterns consistent with the standing-wave pipe motion.