Simulations of isotropic turbulent flows using lattice Boltzmann method with different forcing functions

Three different forcing functions are used with the lattice Boltzmann method (LBM) to simulate the forced isotropic turbulence in periodic boxes at different resolutions ranging from 32(3) to 256(3) grid points using the D3Q19 model. The aims of this study are to examine the effect of using different forcing functions on the LBM stability; to track the development of the turbulent fields at several resolutions, to investigate the effect of the weak compressibility due to change of fluid density on the flow simulations, and to identify the effective force type. The injection is performed through adding the force randomly to the collision term. The three forcing methods depend on sine and cosine as functions of the wave numbers and space. The forcing amplitude values of A = 10(-4) and the relaxation time tau = 0.503 are fixed in all cases. The single relaxation time model is found stable at such values of the forcing amplitude and the relaxation time. However, the development of the turbulent data at the different resolutions needs about 10000 time-steps to reach the required statistical state including clear visualizations of fine scale vortices. Many simulations have been tested using different values of the relaxation time tau and the development of the turbulent fields is found faster with fewer time-steps but the stability of the LBM is broken at some resolutions (not necessary the higher resolution). The statistical features of all fields, such as the Taylor and the Kolmogorov micro-scales, the Taylor Reynolds number, the flatness and the skewness, are calculated and compared with the previous efforts. The worm-like vortices are visualized at all cases and it is found that more fine vortices can be extracted as the resolution increases. The energy spectrum has a reasonable Kolmogorov power law at the resolutions of 128(3) and 256(3), respectively. Results show that the third forcing method that uses a cosine disturbance function has the best statistical features and the finest visualized vortical structures especially at higher resolutions. Extensive discussions about the density field and its evolution with time at different forcing functions, comparison to Navier-Stokes solutions and the time development of the energy spectra for all cases are also carried out.