Multi-relaxation Time Lattice Boltzmann Method Research Articles

Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation-Time Lattice Boltzmann Method

AbstractIn this paper, the power-law fluid flows in a two-dimensional square cavity are investigated in detail with multi-relaxation-time lattice Boltzmann method (MRT-LBM). The influence of the Reynolds number (Re) and the power-law index (n) on the vortex strength, vortex position and velocity distribution are extensively studied. In our numerical simulations, Re is varied from 100 to 10000, and n is ranged from 0.25 to 1.75, covering both cases of shear-thinning and shear-thickening. Compared with the Newtonian fluid, numerical results show that the flow structure and number of vortex of power-law fluid are not only dependent on the Reynolds number, but also related to power-law index.

The use of MRT-lattice Boltzmann method for the prediction of fluid solid flow

Computation of fluid solid flow requires an accurate scheme to capture the moving boundary problems for solid objects moving in a fluid. In this paper, a multi-relaxation time lattice Boltzmann method is coupled with the Newton's second law to predict the flow characteristics around obstacle placed in a channel. The treatment of the curved boundary is based on the conventional bounce-back boundary scheme and interpolations. Good agreement with the previous studies by other methods indicates good applicability of the present scheme.

Topology optimization of multi-component flows using a multi-relaxation time lattice Boltzmann method

We present a topology optimization method to systematically design the layout and shape of flow channels in micro-mixers for miscible fluids under steady-state conditions. The multi component flow is predicted by a multi-relaxation time lattice Boltzmann method (MRT-LBM) which allows independent control of Reynolds and Schmidt numbers. The MRT-LBM is verified against results of a passive scalar finite element advection–diffusion model. The geometry of the flow channels is described by a material distribution approach by varying the porosity of a fictitious material. While this material model penalizes fluid velocity it does not prevent diffusion through porous material. We show that for Péclet numbers greater than 1 the diffusion of fluids through porous material does not significantly affect mixing predictions. The material distribution is optimized by a gradient-based optimization scheme using adjoint sensitivities to compute the derivatives of the objective and constraints. For a two-dimensional model problem, we compare optimization results for various formulations of the design problem. The numerical results illustrate the suitability of the proposed method to optimize micro-mixers and show interesting interdependencies between the porosity model and the formulation of the objective function.

Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics

Lattice Boltmzann Methods (LBM) have been proved to be very effective methods for computational aeroacoustics (CAA), which have been used to capture the dynamics of weak acoustic fluctuations. In this paper, we propose a strategy to reduce the dispersive and disspative errors of the two-dimensional (2D) multi-relaxation-time lattice Boltzmann method (MRT-LBM). By presenting an effective algorithm, we obtain a uniform form of the linearized Navier–Stokes equations corresponding to the MRT-LBM in wave-number space. Using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods, we propose a class of minimization problems to optimize the free-parameters in the MRT-LBM. We obtain this way a dispersion-relation-preserving LBM (DRP-LBM) to circumvent the minimized dispersion error of the MRT-LBM. The dissipation relation precision is also improved. And the stability of the MRT-LBM with the small bulk viscosity is guaranteed. Von Neuman analysis of the linearized MRT-LBM is performed to validate the optimized dispersion/dissipation relations considering monochromatic wave solutions. Meanwhile, dispersion and dissipation errors of the optimized MRT-LBM are quantitatively compared with the original MRT-LBM. Finally, some numerical simulations are carried out to assess the new optimized MRT-LBM schemes.