Effect of the kinetic energy conservation error on unsteady/steady isotropic turbulence: a numerical simulation study

Abstract

This study presents the effects of the conservation error of turbulent kinetic energy on the isotropic turbulence field. Here, the present research focuses on the effects on the unsteady turbulence field in addition to the steady field. This unsteady turbulence field is given by changing the magnitude of the external forcing term using a linear forcing scheme with a sinusoidal function. The conservation error is caused by using the Crank-Nicolson method, which is an implicit time integration method. This result is examined by comparing those with the results with negligible conservation error using the fourth-order Runge-Kutta scheme. For this unsteady turbulence, the period and amplitude of the external forcing term are changed as computational conditions. In contrast to steady turbulence, unsteady turbulence is shown to be affected by turbulent kinetic energy conservation error. These effects are significant when the period is short and the amplitude is large.