Numerical Simulation of Isotropic Turbulence Using a Collocated Approach and a Nonorthogonal Grid System

We studied the effect of using a nonorthogonal grid coordinate system and a finite-volume approach in the simulation of decaying isotropic turbulence. Calculations were performed in distorted periodic cubic boxes and with a turbulent Reynolds number, based on the Taylor microscale and on a root mean square turbulent velocity, of approximately 40. A preliminary study showed that in the nonorthogonal grids some Fourier modes of the discretized derivatives can have greater amplitude or the phase inverted relatively to the modes of the exact derivative, contrary to what occurs with a Cartesian grid system. However, in the simulations, the statistical distributions of velocity, pressure, and longitudinal and lateral velocity derivatives were always identical, regardless of the grid distortion. The temporal evolution of the energy was also similar and the differences at the end of the simulations (after about two eddy turnover times) did not exceed 1%. Furthermore, the grid nonorthogonality affected neither the isotropy of the fields nor the correlation between the vorticity and the principal rates of strain. We concluded that the finite-volume approach in nonorthogonal grid systems may be used in the numerical simulation of complex turbulent flows with either the direct numerical simulation or large-eddy simulation methodologies.