Pseudospectral simulation of turbulent viscoelastic channel flow

Abstract The methodology and validation of direct numerical simulations of viscoelastic turbulent channel flow are presented here. Using differential constitutive models derived from kinetic and network theories, numerical simulations have demonstrated drag reduction for various values of the parameters, under conditions where there is a substantial increase in the extensional viscosity compared to the shear viscosity (Sureshkumar, Beris, Handler, Direct numerical simulation of turbulent channel flow of a polymer solution, Phys. Fluids 9 (1997) 743–755 and Dimitropoulos, Sureshkumar, Beris, Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters, J. Non-Newtonian Fluid Mech. 79 (1998) 433–468). In this work, new results pertaining to the Reynolds stress and the pressure are presented, and the convergence of the pseudospectral algorithm utilized in the simulations, as well as its parallel implementation, are discussed in detail. It is shown that the lack of mesh refinement, or the use of a larger value for the artificial stress diffusivity used to stabilize the conformation tensor evolution equations, introduce small quantitative errors which qualitatively have the effect of lowering the drag reduction capability of the simulated fluid. However, an insufficient size of the periodic computational domain can also introduce errors in certain cases, which albeit usually small, can qualitatively alter various features of the solution.