In this paper, a model has been presented for generating a special ring vortex by applying a nonconservative force with specific distribution through the Navier-Stokes equations. Moreover, the ring's vortical pattern has been compared with the analytical and experimental results. In continuation, the diffusion, dissipation, and dispersion errors of four basic convection term interpolation schemes for the velocity and vorticity field of the vortex ring have been investigated. The simulations are performed for both the small and large time steps. Next, an appropriate discretization scheme for the convection term, and a proper order of time steps for simulating flows that contain ring vortices have been proposed. Finally, the ring vortexes generated by non-conservative force are added to the turbulent channel flow as a bubble induced vortex on carrier flow in two-phase flows, and the drag reduction due to the interaction between ring vortexes and flow vorticity field is observed.

This paper establishes relations between the stability and the high-order truncated corrections for modeling of the mass conservation equation with the two-relaxation-times (TRT) collision operator. First we propose a simple method to derive the truncation errors from the exact, central-difference type, recurrence equations of the TRT scheme. They also supply its equivalent three-time-level discretization form. Two different relationships of the two relaxation rates nullify the third (advection) and fourth (pure diffusion) truncation errors, for any linear equilibrium and any velocity set. However, the two relaxation times alone cannot remove the leading-order advection-d if fusion error, because of the intrinsic fourth-order numerical diffusion. The truncation analysis is carefully verified for the evolution of concentration waves with the anisotropic diffusion tensors. The anisotropic equilibrium functions are presented in a simple but general form, suitable for the minimal velocity sets and the d2Q9, d3Q13, d3Q15 and d3Q19 velocity sets. All anisotropic schemes are complemented by their exact necessary von Neumann stability conditions and equivalent finite-difference stencils. The sufficient stability conditions are proposed for the most stable (OTRT) family, which enables modeling at any Peclet numbers with the same velocity amplitude. The heuristic stability analysis of the fourth-order truncated corrections extends the optimal stability to larger relationships of the two relaxation rates, in agreement with the exact (one-dimensional) and numerical (multi-dimensional) stability analysis. A special attention is put on the choice of the equilibrium weights. By combining accuracy and stability predictions, several strategies for selecting the relaxation and free-tunable equilibrium parameters are suggested and applied to the evolution of the Gaussian hill.

We present a Rayleigh–Taylor mixing rate simulation with an acceleration rate falling within the range of experiments. The simulation uses front tracking to prevent interfacial mass diffusion. We present evidence to support the assertion that the lower acceleration rate found in untracked simulations is caused, at least to a large extent, by a reduced buoyancy force due to numerical interfacial mass diffusion. Quantitative evidence includes results from a time-dependent Atwood number analysis of the diffusive simulation, which yields a renormalized mixing rate coefficient for the diffusive simulation in agreement with experiment. We also present the study of Richtmyer–Meshkov mixing in cylindrical geometry using the front tracking method and compare it with the experimental results.