High-fidelity robust and efficient finite difference algorithm for simulation of polymer-induced turbulence in cylindrical coordinates

Abstract

A high-fidelity finite difference method for simulation of viscoelastic turbulence in cylindrical coordinates has been developed. In this algorithm, the evolution equation for the polymer conformation tensor is discretized by an improved Kurganov–Tadmor (KT) scheme, while the continuity and momentum equations are discretized by a well-established second-order accurate central difference scheme on staggered grids. To minimize the computational cost of the original KT scheme, two novel improvements have been implemented: (i) a sequential ranking strategy to rapidly select the slope-approximation in the original KT scheme, and (ii) a simple criterion to diagnose and in turn assure the positive definiteness of the conformation tensor that obviates the need for CPU intensive eigenvalue calculations. These modifications lead to an algorithm that is twice as fast as the original KT method. This in turn has enabled high-fidelity and efficient larger-scale simulations of viscoelastic turbulent flows in a parallel framework using 2D-domain decomposition, as evinced by benchmark results for two canonical viscoelastic flows, namely, the viscoelastic pipe flows (VPF) and the viscoelastic Taylor–Couette flows (VTCF). To that end, the fidelity and computational efficiency of this algorithm have been demonstrated in a broad range of polymer-induced flow dynamics, namely, elasto-inertial instability in the VPF, polymer-induced drag reduction at high R e in the VTCF, and purely elastic instability in low- R e VTCF. Overall, this algorithm is an efficient and high-fidelity scheme for the simulation of viscoelastic turbulence in a broad range of elastically and/or inertially dominated flows. • A new robust finite-difference method for viscoelastic turbulence is proposed. • High-fidelity simulations are performed using the proposed method. • Strategies to improve computational efficiency are proposed. • Comprehensive validations in cylindrical coordinates are carried out.