International Journal of Modern Physics C

A novel flexible forcing immersed boundary and lattice Boltzmann method (IB-LBM) is introduced in this paper. In the conventional IB-LBM scheme, explicit calculation of the force density term may not guarantee exact satisfaction of the no-slip boundary condition. This produces unphysical streamline penetration into the solid object. In this study, an implicit approach is followed where the force density is obtained from the unknown velocity correction with a unique single Lagrangian velocity correction term and flexible number of forcing steps. The proposed algorithm is computationally efficient and easy for new code development. Also the algorithm is found advantageous for unsteady flow case where no-slip condition is accurately satisfied. Flow past circular cylinder is studied for both steady and unsteady flow cases to validate the proposed scheme.

We assess the Lattice Boltzmann (LB) method versus centered finite-difference schemes for the solution of the advection–diffusion–reaction (ADR) Fisher's equation. It is found that the LB method performs significantly better than centered finite-difference schemes, a property we attribute to the near absence of dispersion errors.

In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Q_x,Q_y,Q_z) family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss–Laguerre, as well as the Gauss–Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.

The lattice Boltzmann method (LBM) is an explicit numerical scheme for the incompressible Navier–Stokes equations (INSE) without integrating the Poisson equation for the pressure. In spite of its merit, the LBM has some drawbacks in accuracy. First, we review drawbacks for three numerical methods based on the LBM. The three methods are the LBM with the Bhatnagar–Gross–Krook model (LBGK), the lattice kinetic scheme (LKS) and the link-wise artificial compressibility method (LWACM). Second, in order to remedy the drawbacks, we propose an improved LKS. The present method incorporates (i) the scheme used in the LWACM for determining the kinematic viscosity, (ii) an iterative calculation of the pressure and (iii) a semi-implicit algorithm, while preserving the simplicity of the algorithm of the original LKS. Finally, in simulations of test problems, we find that the improved LKS eliminates the drawbacks and gives more accurate and stable results than LBGK, LKS and LWACM.

In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO₄ solution.

Spreading of nano-droplets is an interesting and technologically relevant phenomenon, where thermal fluctuations lead to unexpected deviations from well-known deterministic laws. Here, we apply the newly developed fluctuating nonideal lattice Boltzmann (LB) method [M. Gross, M. E. Cates, F. Varnik and R. Adhikari, J. Stat. Mech.2011, P03030 (2011)] for the study of this issue. Confirming the predictions of Davidovich and coworkers [Phys. Rev. Lett.95, 244905 (2005)], we provide the first independent evidence for the existence of an asymptotic, self-similar noise-driven spreading regime in both two- (2D) and three-dimensional (3D) geometry. The cross over from the deterministic Tanner's law, where the drop's base radius b grows (in 3D) with time as b ~ t^1/10 and the noise dominated regime, where b ~ t^1/6 is also observed by tuning the strength of thermal noise.

The stability of flight by flapping wings is investigated by using the immersed boundary-lattice Boltzmann method (IB-LBM). First, the rotational motion with an initial small disturbance is computed, and it is found that the rotational motion is unstable for high Reynolds numbers. Second, we show simple ways to control the rotational and translational motion by bending or flapping the tip of the wing.

The lattice-Boltzmann method (LBM) is used in conjunction with a very large-eddy simulation (VLES) turbulence modeling approach to compute separated flows over backward-facing steps at different wall inclination angles. The Reynolds number Re_H based on the step height H and center-line velocity at the channel inlet u_cl is 64 000. The expansion ratio of the outlet section to the inlet section of the channel is 1.48. Wall inclination angles α considered include 10°, 15°, 20°, 25°, 30° and 90°. The computed flow fields for different inclination angles of the step are assessed against the laser Doppler anemometry (LDA) measurements of Makiola [B. Makiola, Ph.D. Thesis, University of Karlsruhe (1992); B. Ruck and B. Makiola, Flow separation over the step with inclined walls, in Near-Wall Turbulent Flows, eds. R. M. C. So, C. G. Speziale and B. E. Launder (Elsevier, 1993), p. 999.]. In addition to validating the lattice-Boltzmann solution with the experiments, this study also investigates the effects of three dimensionality, the proximity of the inlet to the step, and the grid resolution on the quality of the predictions.

The buoyancy driven exchange flow through the large openings in horizontal partitions occurs in many practical situations such as in enclosed regions with a ceiling opening and a heat source such as fire. The density difference between two compartments arises partly due to difference in composition and partly from the difference in temperature. A heavier fluid located on the top of a lighter fluid and separated by a horizontal vent constitutes a gravitationally unstable system. Horizontal vents produce flow, which are unstable with irregular oscillatory behavior. However, when lower compartment is slightly pressurized the flow becomes stable and unidirectional. A numerical study has been performed to characterize the bi-directional flow and transition to unidirectional flow through a horizontal vent in an enclosure, due to differences in pressure and density across the vent. Fresh and salt water has been considered as working fluids to create density difference across the vent with a pressure field imposed in the lower compartment. The pressure in the lower region was increased to find the critical pressure corresponding to transition to unidirectional from bi-directional flow. Unsteady, 2D axisymmetric, incompressible Navier–Stokes equation along with species, turbulence and continuity equation have been solved with finite volume method using the in-house computational fluid dynamics (CFD) code. Several cases were examined to compute the critical pressure for various density differences for low opening aspect ratio. The code has been validated with reported experiments and used to simulate various other practical cases occurred during fire induced flow through such openings.

We propose a modified direct simulation Monte Carlo (DSMC) method, which extends the validity of DSMC from rarefied to dense system of hard spheres (HSs). To assess this adapted method, transport properties of hard-sphere (HS) systems have been predicted both at dense states as well as dilute, and we observed the excellent accuracy over existing DSMC-based algorithms including the Enskog theory. The present approach provides an intuitive and systematic way to accelerate molecular dynamics (MD) via mesoscale approach.

The entropic lattice Boltzmann method (ELBM) has been demonstrated to bring unconditional stability and accuracy to sub-gird flow simulations. However, the application of ELBM to engineering flows were restricted so far due to the lack of a matching wall boundary condition that retains the accuracy of the method for both resolved and under-resolved simulations. To this end, we show that the recently proposed wall boundary condition for ELBM is reliable and accurate for both these regimes. Three-dimensional (3D) flow past a circular cylinder is taken as a benchmark to show that ELBM is both stable and accurate for range of Reynolds numbers and grid sizes. Several key parameter of this flow are studied in detail.

The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space — tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.