Calculation of isotropic turbulence using a pure Lagrangian vortex method

Abstract

The vortex method is applied to the calculation of a decaying homogeneous isotropic turbulence of Re k = 25, 50 and the results are compared with a spectral method calculation. Vortex method calculations were accelerated by the use of a fast multipole method for periodic boundary conditions. The core spreading method and particle strength exchange were selected as the viscous diffusion scheme. The effect of spatial resolution was examined along with Reynolds number dependence and the effect of spatial adaption of elements.

Direct Numerical Simulation in Two Dimensional Homogeneous Isotropic Turbulence Using Spectral Method

“…2, we can observe that the enstrophy decreases with increase of time, which is also in agreement with the result of Yokota et al [12] for a decaying homogeneous isotropic turbulence. The turbulence dissipation, ε versus time is presented in Fig.…”

“…11 which is about 0.08 at the beginning of the computation (t = 0) and it reaches about 0.32 at the end of calculation. The behavior of the derivative of the skewness in the whole calculation domain is in good agreement with the result of Yokota et al [12]. …”

“…1 we can observe that the total energy or, equivalently the kinetic energy decreases with time until the end of the calculation. The trend of the profile is always decaying which is in agreement with the result of Yokota et al [12], where the kinetic energy spectrum of a decaying homogeneous isotropic turbulence is calculated using a pure Lagrangian vortex method. Fig.…”

Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

“…The rate of energy decay had good agreement with the PSM when spatial adaptation was implemented for their vortex method calculation. Following that, the three-dimensional isotropic turbulence was calculated by Yokota et al [9] using the vortex method and PSM. The kinetic energy decay was in good accordance with that of the PSM when the spatial resolution was sufficient and spatial adaptation [5] was used.…”

“…The diffusion term of Equation (4) is solved by the core spreading method with spatial adaptation [9]. For the calculation of Equations (7) and (11), the shear periodic boundary condition is enforced by using a shear periodic FMM mentioned in Section 2.2.…”