Consistent forcing scheme in the cascaded lattice Boltzmann method

In this paper, we give a more pellucid derivation for the cascaded lattice Boltzmann method (CLBM) based on a general multiple-relaxation-time (MRT) frame through defining a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The applicability of the non-slip rule, the second-order convergence rate in space and the property of isotropy for the consistent forcing scheme is demonstrated through the simulation of several canonical problems. Several other existing force schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework

Algorithm for Computing Excited States in Quantum Theory

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we present a different algorithm: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach. As a new example, application to the Klein-Gordon field theory is shown.Comment: 3 pages, uses Latex and aipproc.cl

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Li et al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/sqrt(a). Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.Comment: 9 figures, 2 tables, accepted by Physical Review E (in press

Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method

In this paper, a central-moment-based lattice Boltzmann (CLB) method for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection-diffusion equation for the temperature field are sloved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. For the flow field, the tedious implementation for CLB method is simplified by using the shift matrix with a simplified central-moment set, and the consistent forcing scheme is adopted to incorporate forcing effects. Compared with several D2Q5 multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Thus a higher Mach number can be used for convection flows, which decreases the computational load significantly. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLB method for incompressible thermal flows is of second-order accuracy in space