Special Issue for the 25th International Conference on Discrete Simulation of Fluid Dynamics (DSFD)

We present quantum Lattice Boltzmann simulations of the Dirac equation for quantum-relativistic particles with random mass. By choosing zero-average random mass fluctuation, the simulations show evidence of localization and ultra-slow Sinai diffusion, due to the interference of oppositely propagating branches of the quantum wavefunction which result from random sign changes of the mass around a zero-mean. The present results indicate that the quantum lattice Boltzmann scheme may offer a viable tool for the numerical simulation of quantum-relativistic transport phenomena in topological materials.

Fibrous filter media are made of small fibers (micro and nanoscale). In these cases, the Knudsen number can be appreciable and the slip phenomenon on the fluid boundary surfaces should be considered. For this purpose, the mesoscopic approach lattice Boltzmann method (LBM) can be applied to predict the flow, with appropriate boundary conditions (BC). This paper analyzes a fibrous microfilter, including the construction of the geometric model from scanning electron microscope (SEM) images, and the comparison with experimental results and macroscopic approach modeling. A slip condition was implemented in open-source code OpenLB, based on specular reflections of the populations. The validation of the proposed boundary condition was carried out by simulations in a 2D channel, disposed at 45 and 90 degrees, and simple cases of a flow around an octagon. The experimental order of convergence (EOC) was evaluated for all cases and the results of the pressure drop around the octagon were compared to data obtained by a macroscopic approach. A good agreement between the pressure drop through the filter media and the results obtained numerically and experimentally was observed. These findings endorse the accuracy of the implemented slip BC and the importance in considering this phenomenon in microscale systems.

The transport and deposition of particles over a fixed obstacle set in a fluid flow is investigated numerically. A two-dimensional model, based on lattice Boltzmann (LB) method and discrete element (DE) method, is used to simulate particle deposition. The corresponding method is two-way coupling in the sense that particle motion affects the fluid flow and reciprocally. The particle capture efficiency, as a function of particle size and Stokes number, is investigated using one-way (effect of the particle on the fluid is not considered) and two-way coupling respectively. The numerical simulations presented in this work are useful to understand the transport and deposition of particles and to predict the single fiber collection efficiency. The effect of obstruction shape on single fiber collection efficiency is investigated with LB-DE methods. Results show that the influence of particle on the flow field cannot be neglected for particles with large size. Numerical results for circular fiber collection efficiency are in good agreement with theoretical prediction and existing correlations. Enhanced collection efficiency is achieved by changing the fiber shape.

Wing planform is one of important factors for lift and thrust generation and enhancement in flapping flight. In this study, we numerically investigate the effect of wing planform on aerodynamic performance of a butterfly-like flapping wing-body model by using the immersed boundary-lattice Boltzmann method. The model flaps downward for generating the lift force and backward for generating the thrust force like an actual butterfly. We calculate the aerodynamic performance such as the lift force, the thrust force, the power expenditure, and the power loading for (i) trapezoidal wing planforms with various taper ratios (ratio of the wing-tip length to the wing-root length), (ii) rectangular wing planforms with various aspect ratios (ratio of the square of the wing length to the wing area), and (iii) an actual butterfly's wing planform at the Reynolds number of 500. As a result for the trapezoidal and rectangular wing planforms, we find that the lift and thrust forces increase at the cost of the power expenditure as the taper ratio increases and as the aspect ratio increases. In addition, it is found that the actual butterfly's wing planform is more efficient than any of the trapezoidal and rectangular wing planforms.

The immersed boundary lattice-Boltzmann lattice-spring method (IBLLM) has previously been implemented to solve several systems involving deformable and moving solid bodies suspended in Navier-Stokes fluids, but these studies have generally been limited in scope by a lack of computing power. In this study a Graphics Processing Unit (GPU) in CUDA Fortran is implemented to solve a variety of systems, including a flexible beam, stretching of a red blood cell (RBC), and an ellipsoid under shear flow. A series of simulations is run to validate implementation of the IBLLM and analyze computing performance. Results demonstrate that an Intel Xeon E5645 fitted with an NVIDIA Tesla K40 graphics card running on a GPU improves computational speed by a maximum of over 80-fold increase in speed when compared with the same processor running on a CPU for solving a system of moderately sized solid and fluid particles. These studies represent the first report on using a single GPU device with CUDA Fortran in the implementation of the IBLLM solver. Incorporation of a GPU while solving with the versatile IBLLM technique will expand the range of complex fluid-solid interaction (FSI) problems that can be solved in a variety of fields.

In this paper, the finite difference weighed essentially non-oscillatory (WENO) scheme is incorporated into the recently developed lattice Boltzmann flux solver (LBFS) to simulate compressible flows. The resultant WENO-LBFS scheme combines advantages of WENO scheme and LBFS, e.g., high-order accuracy, high resolution and physical robustness. Various numerical tests are carried out to compare the performance of WENO-LBFS and that of other WENO-based flux solvers, including the Lax-Friedrichs flux, the modification of the Harten-Lax-van Leer flux, the multi-stage predictor-corrector flux and the flux limiter centered flux. It turns out that WENO-LBFS is able to capture discontinuous profile in shock waves. Comparatively, the WENO-LBFS scheme costs less CPU time and eases programming.

It is important to have detailed knowledge of large scale spacecraft reentering atmospheric disintegration and main structures melting ablation for an accurate estimate of debris spread area. The direct simulation Monte Carlo (DSMC) method is performed to simulate aerothermodynamic characteristics of Tiangong-1 simplified configuration in rarefied transitional regime during its reentry process. The hybrid Cartesian and surface unstructured triangular meshes as well as adaptive refinement are employed to deal with these complex configuration flows. Internal energy excitations and chemical reactions are considered to compute aero heating precisely. A large number of computational difficulties are solved by the DSMC parallel algorithm based on MPI environment. Hypersonic nitrogen flow of Mach 15.6 about a 25/55 deg biconic model is chosen as test cases for validation. The calculated pressure and heating rate distributions have good agreement with the experimental data. Based on the DSMC results of Tiangong-1 shape, the structure stress of solar panels connecting model is analyzed with finite element method. The heat conduction and ablation computations are performed on thin shell structure of spacecraft with one-dimensional model. The height of solar panels broken away from the spacecraft main body is preliminary estimated. The melting ablation of two module structure vehicle is analyzed for different reentering altitudes.

In this work, numerical simulations have been performed to study the shock/ droplet interaction before a standing wall. The research efforts are directed to reveal the influence of the reshock on the flow features and interfacial dynamics. A five-equation model is applied to model the compressible multi-fluid flow with moving interface. The governing equations are solved under an axisymmetric assumption using a finite volume method. By varying the incident shock Mach number ($M_S$) and the distance (L) between the droplet and the wall, the wave motion and the droplet deformation are closely examined for four typical simulations. Also, the underlying physics of some salient flow features and interfacial behavior is discussed. Moreover, the maximum wall pressure is monitored in term that structural damage is possibly induced to the wall as a result of the shock/droplet interaction. The droplet kinematics is examined via the center-of-mass displacement and velocity, to clarify the integral effects of changing $M_S$ and L.

Water management in gas diffusion layer (GDL) and micro porous layer (MPL) poses a great impact on performance of proton exchange membrane fuel cells (PEMFCs). And enhancement of the performance of fuel cells requires an appropriate water balance between the conservation of membrane humidity and the discharge of excess water produced in the cell. The Lattice Boltzmann method (LBM) can enable more straight simulation of fluid flow with complex solid structures, compared with conventional computational fluid dynamics (CFD) method based on Navier-Stokes equations. In this study, the orthorhombic pseudo-potential multiphase lattice Boltzmann method (LBM) is used to investigate liquid water transport in the MPL and GDL of polymer electrolyte membrane fuel cells (PEMFC). And the GDL and MPL structure images are all acquired by the stochastic generation method. We compared the GDL coated by the MPL with different thickness and different porosity. Numerical results confirm that influence of porosity is much greater than the thickness, which can help to improve the GDL and MPL design.

Massively parallel simulation applied multiple graphic processing units (multi-GPUs) is carried out to perform an in-depth investigation on the flow and heat transfer mechanism in film cooling based on hybrid thermal lattice Boltzmann method (HTLBM). For the flow field, multiple-relaxation-time (MRT) collision model is used. A coolant jet is injected at an inclined angle of α=30^◦into a turbulent flat plate boundary layer profile with free-stream Reynolds number of Re = 4000. In our previous work [1], we proposed a three-part definition for the jet-crossflow-interaction region according to the turbulent kinetic energy (TKE) distribution and the unsteady mixing characteristics in each domain were studied qualitatively. In order to further investigate this phenomenon, a more detailed study on unsteady flow and heat transfer characteristics is performed in this work. The results show that the shear domain is dominated by the shearing effect and covered by stable coolant film. In rotating domain, the turbulent intensity increases because of the violent mixing between crossflow and jet flow and the coolant film begins to spread in lateral. All of these cause the rapid decrease in coolant film stability. The great turbulent-dissipation effect in dissipation domain weakens the turbulent intensity and strengthens the fluctuation of spanwise velocity. The cooling performance is very poor.

A numerical scheme capable of modeling fluid behavior on wetting surfaces is developed based on an interface-capturing lattice Boltzmann equation model [Q. Lou and Z. Guo, Phys. Rev. E 91, 013302 (2015)], which has not yet been applied to wetting problems. With the proposed numerical scheme, the spurious densities near the solid surfaces can be eliminated and a wide range of equilibrium contact angles can also be reproduced. Further, the equilibrium contact angle on the solid surface, as a simulation parameter, can be given in advance according to the wettability. Numerical tests, including the dynamics behavior of a liquid drop spreading on a smooth surface and the capillary intrusion, demonstrate that the proposed numerical scheme performs well and can eliminate the spurious densities near the solid surface.

In this paper, we present an improved version of the simplified lattice Boltzmann method on non-uniform meshes. This method is based on the recently-proposed simplified lattice Boltzmann method (SLBM) without evolution of the distribution functions. In SLBM, the macroscopic variables, rather than the distribution functions, are directly updated. Therefore, SLBM calls for lower cost in virtual memories and can directly implement physical boundary conditions. However, one big issue in SLBM is the lattice uniformity, which is inherited from the standard LBM and this makes SLBM only applicable on uniform meshes. To further extend SLBM to non-uniform meshes, Lagrange interpolation algorithm is introduced in this paper to determine quantities at positions where the streaming process is initiated. The theoretical foundation of the interpolation process is that both the equilibrium part and the non-equilibrium part of the distribution functions are continuous in physical space. In practical implementation, the Lagrange interpolation polynomials can be computed and stored in advance, due to which little extra efforts are brought into the computation. Three numerical tests are conducted with good agreements to reference data, which validates the robustness of the present method and shows its potential for applications to non-uniform meshes with curved boundaries.

The three-dimensional (3D) single component multiphase Shan-Chen lattice Boltzmann (LB) model is implemented with the GPU-accelerated algorithm based on the CUDA platform for the simulation of droplet evaporation. It is found that the speed-up of the GPU-accelerated 3D LB model with respect to the CPU-based 3D LB model increases with the computational node number. The maximum speed-up is higher than around 300 when the computational domain is composed of $256^3$ computational nodes. Regarding the calculations performed using the GPU-accelerated 3D LB model that incorporates the operation of data output through CPU, the percentage of computational time consumed by CPU for executing the sequential tasks increases with the computational node number. The model validations are carried out through the comparisons of the simulations with Laplace's law and the $D^2$ law. Then, the GPU-accelerated 3D LB model is applied to simulate the evaporation phenomena of a droplet laying on smooth and rough solid surfaces. It is shown that the contact angle of the evaporating droplet on a smooth solid surface almost remains stable during the evaporation process. For the evaporating droplet sitting on a rough solid surface, however, the time evolution of the contact angle displays obvious oscillations. The simulated morphology evolution of the evaporating droplet sitting on a rough solid surface demonstrates that the oscillations of the contact angle are governed by the stick-slip movement, namely, depinning and receding, of the liquid-gas-solid contact line. This can be attributed to the large hysteresis of the droplet displaying the wetting Wenzel state.

The traditional DSMC method is extended to simulate three-dimensional (3D) rarefied ionization flows around spacecrafts during hypervelocity reentry. The electron mass amplification is utilized and the reaction rates involving electron are modified correspondingly. A weighting factor scheme for trace species is proposed, and its impacts on collision mechanism, the realization of chemical reactions as well as the calculations of macroscopic parameters are considered. The proposed DSMC algorithm is highly efficient in simulating weakly inhomogeneous flows, and its reliability is validated by the comparisons with aerodynamics force test of Shenzhou capsule model in low density wind tunnel, the electron number densities of RAM-C II and Stardust in rarefied transitional flow regimes. The introduction of rare species weighting factor scheme can significantly improves the smoothness of the number density contours of rare species, especially for that of electron in weak ionization case, while it has negligible effect on the macroscopic flow parameters. The ionization characteristics of the Chinese lunar capsule reentry process is analyzed for the first time at the altitudes of 80km, 85km and 90km, and the predicted communication blackout altitude agrees with the actual reentry flight data. The computation reveals that, for blunt body reentry with a speed larger than the second cosmic speed, the main ionization source is the direct collision ionization, and the electron number density is high enough to cause communication blackout in traditional rarefied flow regimes.

Self-propelled jump of droplets is among the most striking phenomena in droplet collisions on substrates. Self-propelled jump phenomena of droplets have been observed in experiments, which have also been reproduced in macro- or mesoscale numerical simulations. However, there have been few previous studies on the phenomena at nanoscales. To unravel the dynamics and mechanisms of nanoscale binary droplet collisions on substrates, head-on collision processes of two identical water droplets with diameters of 10nm on graphite substrates are investigated by molecular dynamics (MD) simulations. By varying the impact Reynolds number of binary droplet collisions on hydrophilic or hydrophobic substrates, we successfully reproduce self-propelled jump of droplets on a super-hydrophobic surface with a contact angle of 143^◦ and a relatively high impact Reynolds number of 17.5. Parametric studies indicate that both high impact Reynolds numbers and high hydrophobicity promote self-propelled jump. Moreover, the criterion based on the Ohnesorge number derived from the mesoscopic self-propelled jump regime is insufficient to precisely predict a nanoscale self-propelled jump phenomenon. For this reason, our study includes the impact Reynolds number and the substrate properties like contact angle as additional criteria to refine and extend the current theory for the self-propelled jump behaviours to nanoscales. The study provides insight into the mechanism of self-propelled jump phenomenon at nanoscales.

High speed particulate flow appears in many scientific and engineering problems. Current work focuses on the situation with volume fraction of particles between 0.001 and 0.5, in which both particle-fluid and particle-particle interactions are important. Based on the stratified multi-phase flow model (Chang & Liou, J. Comput. Phys. 225 (2007), 840-873) with Euler equations, by regarding one phase as solid, a numerical method is developed to conduct direct numerical simulations (DNS) to high speed particulate flows. It is then applied to simulate the problem with a planar shock wave impacting on a particle curtain, but focusing on the initial stage, in which the particles can be regarded as static. 2-D simulations are conducted by keeping the total volume fraction of particles and changing the number of particles. The convergence of shock wave locations and turbulent energy are observed. A 1-D volume-averaged model is also studied and compared with the DNS, which gives effective drag coefficients. A 3-D DNS is conducted to compare with the 2-D DNS and 1-D model, showing that more detailed 3-D DNS studies are needed. The convergent values obtained from current work can be applied to the study of very small particle cases and to the model development.

We present a new lattice Boltzmann formulation for elastic solids and analyse the issue of conservation laws for solids. This new formulation allows tunable Poisson ratio. As a first benchmark problem, we consider an elastic wave propagating in an infinite homogeneous medium with point force and point dipole Ricker wavelet as the source. The method is successful in simulating behavior of elastic wave motion as a function of Poisson ratio.

Molecular dynamics simulations are performed to study the supercritical mixing process of the n-dodecane/nitrogen binary system. Previous studies have shown the existence of supercritical phenomenon under certain conditions in modern propulsion systems such as diesel engines. However, the physical mechanisms and internal driving forces of this phenomenon are still not well understood. In this paper, we attempt to answer this question through simulating the diffusion and evaporation of gaseous nitrogen and liquid phase n-dodecane. It addresses under what conditions the supercritical transition phenomenon happens and what features the supercritical evaporation process has. A unique configuration is constructed to mimic the evaporation of an n-dodecane thin film in an open nitrogen environment under conditions ranging from subcritical to supercritical. The detailed structure of the liquid-vapor interface during the evaporating process is described and the evaporation rate and the interface thickness are estimated, which show differences between subcritical and supercritical evaporation. Results indicate that under relatively high pressure conditions, the liquid surface transitions into supercritical state, and the liquid-vapor interface expands significantly with vanishing surface tension, leading to a diffusion like mixing process. It is shown that the supercritical evaporation would happen under conditions that correspond to the in-cylinder conditions of a turbo-charged engine.

We consider the D1Q3 lattice Boltzmann scheme with an acoustic scale for the simulation of diffusive processes. When the mesh is refined while holding the diffusivity constant, we first obtain asymptotic convergence. When the mesh size tends to zero, however, this convergence breaks down in a curious fashion, and we observe qualitative discrepancies from analytical solutions of the heat equation. In this work, a new asymptotic analysis is derived to explain this phenomenon using the Taylor expansion method, and a partial differential equation of acoustic type is obtained in the asymptotic limit. We show that the error between the D1Q3 numerical solution and a finite-difference approximation of this acoustic-type partial differential equation tends to zero in the asymptotic limit. In addition, a wave vector analysis of this asymptotic regime demonstrates that the dispersion equation has nontrivial complex eigenvalues, a sign of underlying propagation phenomena, and a portent of the unusual convergence properties mentioned above.

In this paper, a numerical investigation on heterogeneous catalysis is performed by means of a Regularized Lattice BGK approach. The effects of different values of the reactant flow Knudsen numbers are evaluated, in terms of conversion efficiency and penetration inside the structure of a nano-porous gold ingot. The results are in line with experimental evidence in the literature and open interesting perspectives for the optimal design of future nano-catalytic devices.