Influence of order enhancement of the Runge-Kutta method on low-order turbulence statistics of incompressible wall turbulence under a second-order central difference scheme

In this study, we attempt to understand the effects of the accuracy order of higher-order Runge-Kutta methods on the turbulence statistics of incompressible wall turbulence. A second-order central difference scheme is used to spatially discretize the governing equations, considering the widely used lower-order spatial discretization. The effects of the difference in the order of the Runge-Kutta scheme are investigated using a turbulent channel flow. The turbulence statistics obtained are compared with those reported in three previous studies. Based on our results, we infer that the rms values of the mean velocity, mean pressure, Reynolds stress, and velocity fluctuation of the turbulent channel flow are not affected by the difference in the accuracy order of the higher-order Runge-Kutta method. The fluctuation of the rms values of static pressure obtained by using the fourth-order Runge-Kutta method were consistent with those obtained in previous studies.