Non-linear response of kinetic energy in an inviscid Taylor-Green flow obtained by OpenFOAM-LES with respect to time increments

This study investigates the conservation error of kinetic energy with respect to time increment using OpenFOAM LES. The energy conservation error is verified using an inviscid Taylor-Green vortex and the effect on energy conservation is checked by varying the time increment by a factor of 30. Differences in the response of turbulent energy conservation between large and small time increments are also verified. Higher order accuracy for time increments is expected when the kinetic energy conservation accuracy is high, however the actual behaviour in OpenFOAM needs to be investigated: as the implicit time integration method is used in OpenFOAM, a non-linear response is expected. As a result, it is evident that kinetic energy is not fully conserved in the inviscid flow of OpenFOAM. The kinetic energy distribution is similar for different time increments, with a different relationship between the conservation error observed in the range of large and small time increments.