An accelerated lattice Boltzmann method for natural convection coupled with convolutional neural network

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

Natural convection flow in rectangular cavities with uniform heat flux side walls and an adiabatic floor and ceiling is investigated. The analytical solution for the evenly heated and cooled infinitely tall cavity, obtained by integrating the energy equation over a certain control volume, is introduced and compared to a full numerical solution for the finite cavity. Numerical solutions have been obtained for cavities with height-to-width ratios of 1 to 10, various values of the heat flux and with parameters appropriate to both air and water. For high enough aspect ratio and/or Rayleigh number the numerical solutions at mid-height of the cavity and the cavity stratification are well predicted by the analytical solution for the infinite cavity. The flow on the cavity side walls is then one dimensional. References Armfeld, S. W., and Patterson, J. C., Direct simulation of wave interactions in unsteady natural convection in a cavity. Int. J. Heat Mass Transfer 34 (1991) 929--940. doi:10.1016/0017-9310(91)90004-X Armfeld, S. W., and Patterson, J. C., Wave properties of natural convection boundary layers. J. Fluid Mech. 239 (1992) 195--211. Desrayaud, G., and Nguyen, T. H., Instabilities themoconvectives dans une cavite a flux imposes, in Douzieme Congres Canadien de Mecanique Appliquee (1989) 716--717. Jiracheewanun, S., Armfield, S. W., Behnia, M., and McBain, G. D., The transient behaviour of a differentially heated cavity with isoflux boundaries, Proc. 15th A'asian Fluid Mechanics Conf. (2004) Paper AFMC00246. Kimura, S. and Bejan, A., The boundary layer natural convection regime in a rectangular cavity with uniform heat flux from the side, J. Heat Transfer 106 (No. 1) (1984) 98--103. Leonard, B. P., A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comp. methods appl. mech. engr. 19 (1979) 59--98. doi:10.1016/0045-7825(79)90034-3 Lietzke, A. F., Theoretical and experimental investigation of heat transfer by laminar natural convection between parallel plates, (NACA, 1955) Report 1223. McBain, G. D., Armfield, S. W. and Jiracheewanun, S., The conduction and convection regimes in a cavity with evenly heated and cooled vertical walls, 8th Australasian Heat and Mass Transfer Conf. (2005). (in press) Norris, S. E. and Armfield, S. W., Solving the Navier--Stokes equations on a workstation cluster, ANZIAM J. 42(E) (2000) C1058--C1075. http://anziamj.austms.org.au/V42/CTAC99/Norr Patterson, J. C. and Armfield, S. W., Transient features of natural convection in a cavity, J. Fluid Mech. 219 (1990) 469--497. Patterson, J. and Imberger, J., Unsteady natural convection in a rectangular cavity, J. Fluid Mech. 100 (1980) 65--86.

Topology optimization of natural convection using porous metal foam based on the adjoint lattice Boltzmann method and level set method

The Lattice Boltzmann Method (LBM) is an approach for modeling mesoscopic fluid flow and heat transfer, based on modeling distributions of particles moving and colliding on a lattice. Using a perturbative formulation of the Boltzmann equation, it scales to the macroscopic Navier–Stokes equation. We simulate natural thermal convection via LBM in a 2D rectangular box being heated from below and cooled from above, and use the results as training, testing, and generalization datasets to build a deep learning model. GoogLeNet, a convolutional neural network, is used to classify the simulation results based on two parameters: Rayleigh (Ra) and Prandtl (Pr) numbers, from a single snapshot of either the entire modeling field of resolution 1024×1024, or a 224×224 crop. For each fixed Pr in a range from 1 to 128, increasing by a factor of 2, we estimate Ra with an accuracy varying from 40% to 90%, depending on the chosen augmentation strategy. For each fixed Ra in the range from 105 to 109, increasing of a factor 10, the method predicts Pr with a systematically lower accuracy ranging from 30% to 80%. This approach has great potential for industrial applications like being able to control the industrial flow or scientific research on geophysical ones including the transport of heat in the earth’s interiors, ocean, and atmosphere.

Context. Solving hydrodynamic problems is associated with high computational complexity and therefore requires considerable computing resources and time. The proposed approach makes it possible to significantly reduce the time for solving such problems by applying a combination of two improved modeling methods.
 Objective. The goal is to create a comprehensive hydrodynamic modeling method that requires significantly less time to determine the dynamics of the velocity field by using the modified lattice Boltzmann method and the pressure distribution by using a convolutional neural network.
 Method. A method of hydrodynamic modeling is proposed, which realizes the synergistic effect arising from the combination of the improved lattice Boltzmann method and a convolutional neural network with a specially adapted structure. The essence of the method consists of implementing a sequence of iterations, each of which simulates the process of changing parameters when moving to the next time layer. Each iteration includes a predictor step and a corrector step. At the predictor step, the lattice Boltzmann method works, which allows us to obtain the field of fluid velocities in the working area at the next time layer using the field of velocities at the previous layer. At the corrector step, we apply an improved convolutional neural network trained on a previously created data set. Using a neural network allows us to determine the pressure distribution on a new time layer with a predetermined accuracy. After adding the fluid compressibility correction on the new time layer, we get a refined value of the velocity field, which can be used as initial data for applying the lattice Boltzmann method at the next iteration. Calculations stop when the specified number of iterations is reached.
 Results. The operation of the proposed method was studied on the example of modeling fluid movement in a fragment of the human gastrointestinal tract. The simulation results showed that the time spent implementing the simulation process was reduced by 6–7 times while maintaining acceptable accuracy for practical tasks.
 Conclusions. The proposed hydrodynamic modeling method with a convolutional neural network and the lattice Boltzmann method significantly reduces the time and computing resources required to implement the modeling process in areas with complex geometry. Further development of this method will make it possible to implement real-time hydrodynamic modeling in threedimensional domains.

Modal global linear stability analysis of thermal convection is performed with the linearized lattice Boltzmann method (LLBM). The onset of Rayleigh–Bénard convection in rectangular cavities with conducting and adiabatic sidewalls and the instability of two-dimensional (2-D) and three-dimensional (3-D) natural convection in cavities are studied. The method of linearizing the local equilibrium probability distribution function that was first proposed by Pérez et al. (Theor. Comp. Fluid Dyn., vol. 31, 2017, pp. 643–664) is extended to solve the coupled linear Navier–Stokes equations together with the linear energy equation in this work. A multiscale analysis is also performed to recover the macroscopic linear Navier–Stokes equations from the discrete lattice Boltzmann equations for both the single and multiple relaxation time models. The present LLBM is implemented in the framework of the Palabos library. It is validated by calculating the linear critical value of 2-D natural convection that the LLBM with the multiple relaxation time model has an error less than 1 % compared with the spectral method. The instability mechanism of the flow is explained by kinetic energy transfer analysis. It is shown that the buoyancy mechanism and inertial mechanism tend to stabilize the Hopf bifurcation of the 2-D natural convection at Pr < 0.08 and Pr > 1, respectively. For 3-D natural convection, subcritical bifurcation of the Hopf type is found for low-Prandtl-number fluids (Pr < 0.1).

Purpose – This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls is cooled isothermally while the other is heated by a uniform or linear heat flux whose average is located at mid-height of the wall. The paper aims to discuss these issues. Design/methodology/approach – The governing equations are discretized by the finite volume method and solved, in transient regime, by using the SIMPLE algorithm. Findings – The flow structure, air temperature field, local convective heat flux on the cold wall, variation of the temperature along the heated wall as well as its average and its maximum are analyzed for various combinations of the controlling parameters. These parameters are the linear heat flux slope γ (γ=0, 1 and −1, for a uniform, increasing and decreasing heat flux, respectively), the average Rayleigh number Ra m (103Ra m 3×104) and the aspect ratio A (10A80). It was found that for a given A and Ra m , the highest (lowest) mean temperature of the hot wall is obtained when the linear heating is descending (ascending). While the maximum temperature increases with the three controlling parameters. Practical implications – Accurate correlations which allow calculating the average and maximum temperatures of the heated wall are developed for each type of heating. Also, an empirical relationship for the position of the maximum temperature is provided for γ=−1. Originality/value – Despite its fundamental and practical interest, natural convection in cavities with 10A80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.

Temperature field prediction for various porous media considering variable boundary conditions using deep learning method

Three-dimensional topology optimization of natural convection using double multiple-relaxation-time lattice Boltzmann method

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ≤ Ra ≤ 1000), the internal heating and the local exponent parameters (0 ≤ γ ≤ 5), (1 ≤ λ ≤ 3), the wall to porous thermal conductivity ratio (0.44 ≤ Kr ≤ 9.9) and the ratio of wall thickness to its width (0.02 ≤ D ≤ 0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio.

Three-dimensional natural convection and radiation in a rectangular cavity with one active vertical wall

Natural convection in cavities with constant flux heating at the bottom wall and isothermal cooling from the sidewalls

Magnetic resonance imaging (MRI)-guided radiation therapy (RT) treatment planning is limited by the fact that the electron density distribution required for dose calculation is not readily provided by MR imaging. We compare a selection of novel synthetic CT generation algorithms recently reported in the literature, including segmentation-based, atlas-based and machine learning techniques, using the same cohort of patients and quantitative evaluation metrics. Six MRI-guided synthetic CT generation algorithms were evaluated: one segmentation technique into a single tissue class (water-only), four atlas-based techniques, namely, median value of atlas images (ALMedian), atlas-based local weighted voting (ALWV), bone enhanced atlas-based local weighted voting (ALWV-Bone), iterative atlas-based local weighted voting (ALWV-Iter), and a machine learning technique using deep convolution neural network (DCNN). Organ auto-contouring from MR images was evaluated for bladder, rectum, bones, and body boundary. Overall, DCNN exhibited higher segmentation accuracy resulting in Dice indices (DSC) of 0.93±0.17, 0.90±0.04, and 0.93±0.02 for bladder, rectum, and bones, respectively. On the other hand, ALMedian showed the lowest accuracy with DSC of 0.82±0.20, 0.81±0.08, and 0.88±0.04, respectively. DCNN reached the best performance in terms of accurate derivation of synthetic CT values within each organ, with a mean absolute error within the body contour of 32.7±7.9HU, followed by the advanced atlas-based methods (ALWV: 40.5±8.2HU, ALWV-Iter: 42.4±8.1HU, ALWV-Bone: 44.0±8.9HU). ALMedian led to the highest error (52.1±11.1HU). Considering the dosimetric evaluation results, ALWV-Iter, ALWV, DCNN and ALWV-Bone led to similar mean dose estimation within each organ at risk and target volume with less than 1% dose discrepancy. However, the two-dimensional gamma analysis demonstrated higher pass rates for ALWV-Bone, DCNN, ALMedian and ALWV-Iter at 1%/1mm criterion with 94.99±5.15%, 94.59±5.65%, 93.68±5.53% and 93.10±5.99% success, respectively, while ALWV and water-only resulted in 86.91±13.50% and 80.77±12.10%, respectively. Overall, machine learning and advanced atlas-based methods exhibited promising performance by achieving reliable organ segmentation and synthetic CT generation. DCNN appears to have slightly better performance by achieving accurate automated organ segmentation and relatively small dosimetric errors (followed closely by advanced atlas-based methods, which in some cases achieved similar performance). However, the DCNN approach showed higher vulnerability to anatomical variation, where a greater number of outliers was observed with this method. Considering the dosimetric results obtained from the evaluated methods, the challenge of electron density estimation from MR images can be resolved with a clinically tolerable error.

RETRACTED: Numerical modelling of free convection in a symmetrical cone using MRT LB model combined with experimental properties of TiO2-water

In this work, the distinct lattice spring model (DLSM) and the lattice Boltzmann method (LBM) are coupled together to simulate hydraulic fracturing problems. As the DLSM and LBM are both lattice modelling methods, the lattice meshes in these two systems are simply overlapped, which results in the same resolution in both the DLSM and LBM. The momentum exchange bounce-back algorithm is used to evaluate the forces exerted on the solid particles. Moreover, the calculation step in the LBM and DLSM is synchronised for prompt updates of fluid–solid interactions. The coupled model is further validated through a series of benchmarks. Finally, the coupled model shows its ability to simulate hydraulic fracturing in formations with complex discrete fracture networks.