Development of 2-D and 3-D Double-Population Thermal Lattice Boltzmann Models

A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit

The last decade the Lattice Boltzmann method has evolved into a powerfull solver for flow through porous media, where the solid phase is represented fully resolved on the computational grid (Hill, 2001). Packed and stored fresh agricultural produce are frequently modeled as porous media and therefore we envision Lattice Boltzmann to be an important tool for simulating heat and mass transport in these systems via forced or natural convection. However, practical package and storage systems have too large lengthscales for fully resolved simulations. Consequently, simulations on the full system scale have to be performed at the volume-averaged scale. For the volume-averaged scale closure relations are needed such as the drag force, effective diffusivity or conductivity. Also here Lattice Boltzmann can play a vital role. Lattice Boltzmann is also capable of simulations at the volume-averaged scale, though it has not frequently used for this scale. With this capability, we can build a multiscale simulation approach, similar to what is developed for fluidized beds (van der Hoef, 2004). In this contribution we will present the general framework, and applications of Lattice Boltzmann to forced flow through package with spherical produce (fully resolved), natural convection in bulk containers of seed potatoes (volume-averaged) (van der Sman,1997 & 1999), and some benchmark problems like natural convection in cavity (van der Sman, 2006) and flow in a channel with a porous layer (Beavers and Joseph benchmark). References o Hill R.J., Koch D.L., and Ladd A.J.C. Moderate-Reynolds-number flows in ordered and random arrays of spheres JOURNAL OF FLUID MECHANICS 448: 243-278 (2001). o van der Hoef M.A., Annaland M.V., Kuipers J.A.M. Computational fluid dynamics for dense gas-solid fluidized beds: a multi-scale modeling strategy. CHEMICAL ENGINEERING SCIENCE 59 (22-23): 5157-5165 (2004). o van der Sman R.G.M. Solving the vent hole design problem for seed potato packagings, with the Lattice Boltzmann scheme. INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 11 (3-4): 237-248 (1999). o VanderSman R.G.M. Lattice-Boltzmann scheme for natural convection in porous media INTERNATIONAL JOURNAL OF MODERN PHYSICS C 8 (4): 879-888 (1997) o van der Sman R.G.M. Lattice Boltzmann scheme for natural convection on square and rectangular grids. in revision Phys. Rev. E (2006). IUFoST 2006 DOI: 10.1051/IUFoST:20060990

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

Modified lattice Boltzmann scheme for nonlinear convection diffusion equations

Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

A lattice Boltzmann (LB) simulation strategy is proposed for the incompressible transport phenomena occurring during macroscopic solidification of pure substances. The proposed model is derived by coupling a passive scalar-based thermal LB model with the classical enthalpy–porosity technique for solid–liquid phase-transition problems. The underlying hydrodynamics are monitored by a conventional single-particle density distribution function (DF) through a kinetic equation, whereas the thermal field is obtained from another kinetic equation which is governed by a separate temperature DF. The phase-changing aspects are incorporated into the LB model by inserting appropriate source terms in the respective kinetic equations through the most formal technique following the extended Boltzmann equations along with an appropriate enthalpy updating scheme. The proposed model is validated extensively with one- and two-dimensional solidification problems for which analytical and numerical results are available in the literature, and finally, it is used for solving a benchmark problem, the Bridgman crystal growth in a square crucible.

Lattice Boltzmann simulations of 3D crystal growth: Numerical schemes for a phase-field model with anti-trapping current

A novel approach is proposed in the present study, which combines the lattice Boltzmann method (LBM) with convolutional neural networks and is suitable for square cavity natural convection and conjugate natural convection problems, exhibiting remarkable acceleration capabilities and potentials. The density distribution function obtained from LBM at time t and the temperature distribution function at time t+Δt under different Rayleigh numbers (Ra) are, respectively, utilized as input and output datasets for training and comparison in three convolutional neural networks, aiming to select the optimal coupling model, namely, half-Res-Unet. The coupling model can accurately simulate the natural convection in a square cavity within six times the upper limit of the Ra under the training condition, which can save the central processing unit (CPU) calculation time and the iteration steps by up to 29.2% and 30.3%, respectively. The coupling model is further extended in the current study to incorporate conjugate natural convection, enabling the accurate simulation of temperature distribution under training conditions with a thermal conductivity ratio (Ka) of 25 and an upper limit of Ra increased by 20 times. The corresponding maximum relative errors for the average Nusselt numbers (Nu) are found to be 1.8% and 0.7%, respectively, providing strong evidence for the generalization capability of the coupling model. Furthermore, the coupling model demonstrates a remarkable acceleration performance, as evidenced by its ability to reduce the CPU calculation time by up to 39.6% and iteration steps in the simulation process by 36.5%. It offers valuable insights into the integration of LBM with machine learning techniques, thereby enhancing the computational efficiency of LBM.

In this paper, an alternative multiple-relaxation-time lattice Boltzmann (LB) scheme for conjugate heat transfer is proposed. We have derived the correct energy governing equationfrom the first law of thermodynamics and clarified that the thermal boundary for conjugate heat transfer should be the continuity of the conductive heat flux, which is essential to guarantee Galilean invariance. The development of the present model has two distinct features. First, the temperature evolution equationis modified to include the effect of the specific heat capacity. Second, the convection term is considered as a source term and is calculated in moment space, thus preserving the inherent advantages of the LB method without finite difference calculations. To verify the thermal governing equations, we conduct numerical simulations of heat conduction in a moving rod configuration with varying thermal capacities. Furthermore, to validate the present model's in accuracy, we examine several benchmark problems, including the effective thermal conductivity of parallel and series dual-component materials, steady and unsteady coupled heat transfer in horizontal interface channels, stable heat conduction in a two-layer annulus, natural convection in a square cavity with 16 solid blocks, and thermocapillary flow with two superimposed planar fluids. In the realm of application research, we apply our model to simulate the cooling process in random porous media. The results demonstrate that our model achieves satisfactory accuracy and exhibits a second-order convergence rate in space. The simulation results show the potential of the current LB method to simulate complex applications, highlighting its versatility and accuracy.

A novel coupled lattice Boltzmann model for low Mach number combustion simulation

A three-dimensional model of wave interactions with permeable structures using the lattice Boltzmann method

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Deep learning assisted anode porous transport layer inverse design for proton exchange membrane water electrolysis

I present two novel thread-safe in-place streaming schemes for the lattice Boltzmann method (LBM) on graphics processing units (GPUs), termed Esoteric Pull and Esoteric Push, that result in the LBM only requiring one copy of the density distribution functions (DDFs) instead of two, greatly reducing memory demand. These build upon the idea of the existing Esoteric Twist scheme, to stream half of the DDFs at the end of one stream-collide kernel and the remaining half at the beginning of the next, and offer the same beneficial properties over the AA-Pattern scheme—reduced memory bandwidth due to implicit bounce-back boundaries and the possibility of swapping pointers between even and odd time steps. However, the streaming directions are chosen in a way that allows the algorithm to be implemented in about one tenth the amount of code, as two simple loops, and is compatible with all velocity sets and suitable for automatic code-generation. The performance of the new streaming schemes is slightly increased over Esoteric Twist due to better memory coalescence. Benchmarks across a large variety of GPUs and CPUs show that for most dedicated GPUs, performance differs only insignificantly from the One-Step Pull scheme; however, for integrated GPUs and CPUs, performance is significantly improved. The two proposed algorithms greatly facilitate modifying existing code to in-place streaming, even with extensions already in place, such as demonstrated here for the Free Surface LBM implementation FluidX3D. Their simplicity, together with their ideal performance characteristics, may enable more widespread adoption of in-place streaming across LBM GPU codes.