Reduced conservation error of kinetic energy using a Runge-Kutta algorithm with reduced numerical dissipation

This paper describes an approach that reduces the error in the conservation law of velocity fluctuation intensities and turbulent kinetic energy resulting from a numerical analysis of incompressible flow. The optimized fourth-order Runge-Kutta method used to analyze acoustic problems in previous studies was used here to reduce the numerical dissipation. In order to strictly validate the conservation law of velocity fluctuation intensities and turbulent kinetic energy, the authors used a periodic box filled with an inviscid flow, where velocity fluctuation intensities and turbulent kinetic energy could be analytically held. By using the optimized Runge-Kutta method, the numerical dissipation, which is the error in conservation laws, is of the order of 1/100. The reduction in the numerical dissipation shown in this study increased with an increasing time increment. To investigate the effect of numerical dissipation, higher-order statistics of turbulent kinetic energy were calculated. This study also derived a simple mathematical form to estimate the conservation error of higher-order statistics for turbulent kinetic energy.