We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well established Bouzidi, Firdaouss, and Lallemand (2001) boundary condition for curved walls, despite its local nature. The method also proves to be suitable to simulate moving rigid objects or immersed surfaces either with or without prescribed motion. The core idea of the new approach is to generalize the description of boundary conditions that combine bounce-back rule with interpolations and to enhance them by limiting the information involved in the interpolation to a close proximity of the boundary.
In this work, we propose a family of single-node second-order boundary schemes for the lattice Boltzmann method with general collision terms. The construction of the schemes is quite universal and simple, it does not involve concrete lattice Boltzmann models and uses the half-way bounce-back rule as a central step. The constructed schemes are all second-order accurate if so is the bounce-back rule. In addition, the proposed schemes have good stability thanks to convex combinations. The accuracy and stability of several specific schemes are numerically validated for multiple-relaxation-time mod…
A concise theoretical framework, the $\textit{partial}$ Gauss-Hermite quadrature (pGHQ), is established for constructing on-node lattices of the lattice Boltzmann (LB) method under a Cartesian coordinate system. Comparing with existing approaches, the pGHQ scheme has the following advantages: $\textbf{a).}$ extremely concise algorithm, $\textbf{b).}$ unifying the constructing procedure of symmetric and asymmetric on-node lattices, $\textbf{c).}$ covering full-range quadrature degree of a given discrete velocity set. We employ it to search the local optimal and asymmetric lattices for $\left\{ …
This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid-gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in t…
In this paper, a new progressive mesh algorithm is introduced in order to perform fast physical simulations by the use of a lattice Boltzmann method (LBM) on a single-node multi-GPU architecture. This algorithm is able to mesh automatically the simulation domain according to the propagation of fluids. This method can also be useful in order to perform various types of simulations on complex geometries. The use of this algorithm combined with the massive parallelism of GPUs allows to obtain very good performance in comparison with the static mesh method used in literature. Several simulations a…
Significant improvements in the computational performance of the lattice-Boltzmann (LB) model, coded in FORTRAN90, were achieved through application of enhancement techniques. Applied techniques include optimization of array memory layouts, data structure simplification, random number generation outside the simulation thread(s), code parallelization via OpenMP, and intra- and inter-timestep task pipelining. Effectiveness of these optimization techniques was measured on three benchmark problems: (i) transient flow of multiple particles in a Newtonian fluid in a heterogeneous fractured porous do…
In this work, we improve the accuracy and stability of the lattice Boltzmann model for the Kuramoto-Sivashinsky equation proposed in \cite{2017_Otomo}. This improvement is achieved by controlling the relaxation time, modifying the equilibrium state, and employing more and higher lattice speeds, in a manner suggested by our analysis of the Taylor-series expansion method. The model's enhanced stability enables us to use larger time increments, thereby more than compensating for the extra computation required by the high lattice speeds. Furthermore, even though the time increments are larger than…
In this paper, a boundary scheme is proposed for the two-dimensional five-velocity (D2Q5) lattice Boltzmann method with heterogeneous surface reaction, in which the unknown distribution function is determined locally based on the kinetic flux of the incident particles. Compared with previous boundary schemes, the proposed scheme has a clear physical picture that reflects the consumption and production in the reaction. Furthermore, the scheme only involves local information of boundary nodes such that it can be easily applied to complex geometric structures. In order to validate the accuracy of…
Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation
School of Computational Science and Engineering, Georgia Institute of Technology（计算科学与工程学院，佐治亚理工学院）；Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology（士兵纳米技术研究所，麻省理工学院）
The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations show that the method reaches very low temperatures, at which the liquid-gas density ratio is more than 10^14, while the thermodynamic consistency is still preserved. Decoupling the mesh space from the momentum space through a proportional coefficient, a smaller mesh step provides denser lattice nodes to exactly describe the transition region and the resultin…
We present a novel method for fluid structure interaction (FSI) simulations where an original 2nd-order curved space lattice Boltzmann fluid solver (LBM) is coupled to a finite element method (FEM) for thin shells. The LBM can work independently on a standard lattice in curved coordinates without the need for interpolation, re-meshing or an immersed boundary. The LBM distribution functions are transformed dynamically under coordinate change. In addition, force and momentum can be calculated on the nodes exactly in any geometry. Furthermore, the FEM shell is a complete numerical tool with imple…
The LBM is combined with the Volume Penalization (VP LBM) approach to simulate flows in the presence of obstacles. The single relaxation time LBM and the multiple relaxation time LBM are used. For cases where the fluid motion is enhanced by moving boundaries, the comparison of our results with analytical results is satisfactory. The flow around a cylinder at a relatively high Reynolds number is also calculated. For that case,the VP LBM method was parallelized. A comparison of our results with those found in the literature, demonstrates the reliability of the VP LBM to treat complex flows.
The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular boundary scheme for treating nonslip boundaries. However, this scheme leads to staircase-shaped boundaries for curved walls. Therefore many curved boundary schemes have been proposed, but mostly suffer from mass leakage at the curved boundaries. Several correction schemes have been suggested for simulating single-phase flows, but very few discussions or studies have been made for two-phase LB simulations with curved boun…
The lattice Boltzmann method (LBM) has shown its promising capability in simulating microscale gas flows. However, the suitable boundary condition is still one of the critical issues for the LBM to model microgaseous flows involving curved geometries. In this paper, a local boundary condition of the LBM is proposed to treat curved solid walls of microgaseous flows. The developed boundary treatment combines the Maxwellian diffuse reflection scheme and a single-node boundary scheme which contains a free parameter as well as the distance ratio. The curved boundary condition is analyzed within the…
Gas separation of a binary gaseous mixture is one of characteristic phenomena in the micro-scale flows that differ from the conventional size flows. In this work, the separation in a binary gas mixture flows through a microchannel is investigated by the lattice Boltzmann method with a diffuse-bounce-back (DBB) boundary condition. The separation degree and rate are measured in the He--Ar and Ne--Ar systems for different mole fractions, pressure ratios, and Knudsen numbers. The results show that the separation phenomenon in the He--Ar mixture is more obvious than that in the Ne--Ar mixture at th…
Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann (LB) model that describes a two-dimensional ($2D$) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner transport upwind (CTU) numerical scheme on large square lattices (up to $6144 \times 6144$ nodes). The numerical viscosity and the regularization of the model are discussed for first and second order CTU schemes finding that the lat…
A new lattice Boltzmann model for reactive ideal gas mixtures is presented. The model is an extension to reactive flows of the recently proposed multi-component lattice Boltzmann model for compressible ideal gas mixtures with Stefan-Maxwell diffusion for species interaction. First, the kinetic model for the Stefan--Maxwell diffusion is enhanced to accommodate a source term accounting the change of the mixture composition due to chemical reaction. Second, by including the heat of formation in the energy equation, the thermodynamic consistency of the underlying compressible lattice Boltzmann mod…
Fluid-particle systems are very common in many natural processes and engineering applications. However, accurately and efficiently modelling fluid-particle systems with complex particle shapes is still a challenging task. Here, we present a numerical model that combines the advantages of Lattice Boltzmann Method (LBM) in solving complex flow problems and the capability of the recently introduced Metaball Discrete Element Method (MDEM) in handling non-spherical particle shapes. A sharp interface coupling scheme is developed and the numerical instability issues due to the discontinuity of interf…
