On the performances of standard and kinetic energy preserving time-integration methods for incompressible-flow simulations

TL;DR

This paper analyzes the impact of energy-preserving time-integration methods on large-eddy simulations of incompressible turbulence, showing pseudo-symplectic schemes improve accuracy and reduce computational costs compared to standard Runge-Kutta methods.

Contribution

It introduces and evaluates pseudo-symplectic Runge-Kutta schemes for incompressible flow simulations, demonstrating their advantages over traditional methods.

Findings

Higher-order pseudo-symplectic methods reduce temporal errors.

Standard RK schemes can distort energy spectra in turbulence.

Pseudo-symplectic schemes offer cost-effective accuracy improvements.

Abstract

The effects of kinetic-energy preservation errors due to Runge-Kutta (RK) temporal integrators have been analyzed for the case of large-eddy simulations of incompressible turbulent channel flow. Simulations have been run using the open-source solver Xcompact3D with an implicit spectral vanishing viscosity model and a variety of temporal Runge-Kutta integrators. Explicit pseudo-symplectic schemes, with improved energy preservation properties, have been compared to standard RK methods. The results show a marked decrease in the temporal error for higher-order pseudo-symplectic methods; on the other hand, an analysis of the energy spectra indicates that the dissipation introduced by the commonly used three-stage RK scheme can lead to significant distortion of the energy distribution within the inertial range. A cost-vs-accuracy analysis suggests that pseudo-symplectic schemes could be used to attain results comparable to traditional methods at a reduced computational cost.