Parallelism of MRT Lattice Boltzmann Method based on Multi-GPUs

The aim of the present work is to conduct an evaluation of the ability of Single Relaxation Time (SRT) and Multi Relaxation Time (MRT) formulations of Lattice Boltzmann Method (LBM) to estimate permeability of a porous sample from numerical simulations in the pore scale. Fluid flow is simulated through digitized micro-tomographic images obtained using accurate imaging techniques. The dependence of the permeability calculated on the grid resolution, method used and the variable parameters in the method are studied. The mesoscopic nature of the LBM formulation facilitates the accurate computation of the property values from the pore scale simulation. However, it is observed that use of SRT LBM might not give a viscosity independent prediction of permeability due to numerical errors inherent in the method. Instead, the MRT LBM is found to give accurate predictions which are less dependent on viscosity with appropriately selected relaxation parameter matrix. Moreover, the effect of grid resolution selected on the accuracy of permeability values predicted is closely studied for both SRT and MRT. The conclusions obtained could be of use in predicting permeability for macroscopic flow calculations and realistic reconstruction of the pore geometry making these studies important from academic and industrial viewpoints.

Groundwater flow simulation has become one of the top international issues in new generation of environmental applications. When managing large-scale groundwater flow problems, the intensive computational ability and large amounts of memory space required for modeling are the main bottlenecks for researchers. In order to solve three-dimensional large-scale groundwater flow problems more rapidly, the Open MP was adopted to parallelize the preconditioned conjugate gradient (PCG) algorithm in this paper. And this paper carried out a numerical experiment of the three-dimensional groundwater flow model on a computer with four cores. Based on the numerical experiment, it is found that the execution time of the original serial PCG program is about 1.74 to 2.86 times of the parallel PCG program executed with different number of threads. The experimental results also demonstrate that the PCG solver based on Open MP is an effective way for solving large-scale three-dimensional groundwater flow problem.

In this study we evaluate how an insulated vertical strip functions as a heat regulating element to govern fluid motion together with heat transfer in square cavities. In previous studies, the researchers have given a limited attention to investigating the insulated strips with the use of the multi-relaxation time lattice Boltzmann method. The vertical strip divides the cavity exactly in the middle as both walls of the enclosure operate with oppositely moving lids having the upper wall heated and the lower one cold. The remaining walls within the enclosure hold adiabatic characteristics. The behavior of flow and heat transfer within the enclosure are governed by the principles of mass, momentum, and energy conservation, stated via nonlinear partial differential equations along with relevant boundary conditions. To simulate these phenomena, the D2Q9 lattice methods of the multi-relaxation time lattice Boltzmann method are employed, considering the key dimensionless parameters which include the Grashof numbers from 104 to 5 × 105, the Richardson numbers varying between 0.1 and 100, and the Prandtl numbers ranging from 0.7 to 7. As the Grashof number increases, it promotes greater separation between the dominant vertical structures, pushing them toward the cavity walls and inducing secondary re-circulation regions in the central area. When the Richardson number receives becomes higher, it generates the strengthened buoyancy forces that squeeze the temperature contours while reshaping the thermal distribution pattern over the entire cavity domain. With rising the Grashof number, the average local Nusselt number displays a general trend for increase but exhibits low variation with changes in the Richardson number.

Detailed simulations of flow around various prolate spheroids are performed using multi-relaxation time lattice Boltzmann method (LBM). The simulations are performed in the Reynolds numbers range 0.1≤Re≤2000 at different incident angles 0∘≤ϕ≤90∘ for various prolate spheroids of aspect ratios 1≤λ≤8. The Re is based on the volume equivalent sphere diameter. From the simulations, accurate correlations for average drag, lift and torque coefficients (CD, CL, and CT respectively) are proposed. The mean deviations between the correlations and the simulation data for CD, CL, and CT are 2%, 6.5%, and 4.7% respectively. Furthermore, the correlations are fitted with the physics in mind such that they can be extrapolated beyond the regimes simulated. The fits are designed such that correlations reduce to analytical (CD and CL) solutions available for prolate spheroids in the limit Re≈0. At high Re, the correlations mimic the asymptotic flattening of CD as for spheres and therefore, we expect the correlations to be valid until the critical Re (≈105). Furthermore, extensive comparison of our correlations with other high-fidelity simulations from literature demonstrate the accuracy of our work compared to other correlations from literature. This work enables researchers to perform accurate unresolved Euler-Lagrangian simulations for a wide range of elongated particles.

A multi-relaxation time lattice Boltzmann method (MRT-LBM) fluid flow analysis code is developed based on a two-dimensional D2Q9 lattice model and sub-grid eddy viscosity model of Smagorinsky. Benchmarking of the MRT-LBM is performed for a turbulent flow over staggered tube bundles at Reynolds number of 18,000and compared with standard k-ω turbulence and large eddy simulation (LES). The accuracy of the present MRT-LBM with respect to the mean velocity profiles is found to be reasonably acceptable and even comparable to the LES whereas the computational efficiency is superior.

Present research deals with multiphysics, pore-scale simulation of Li–O2 battery using multirelaxation time lattice Boltzmann method. A novel technique is utilized to generate an idealized electrode–electrolyte porous media from the known macroscopic variables. Present investigation focuses on the performance degradation of Li–O2 cell due to the blockage of the reaction sites via Li2O2 formation. Present simulations indicate that Li–air and Li–O2 batteries primarily suffer from mass transfer limitations. The study also emphasizes the importance of pore-scale simulations and shows that the morphology of the porous media has a significant impact on the cell performance. While lower porosity provides higher initial current, higher porosity maintains sustainable output.

MRT lattice Boltzmann method for 2D flows in curvilinear coordinates

A novel muscle-driven method (MDM) with its corresponding Compute Unified Device Architecture parallel computational code is newly developed to mimic shortening and lengthening of muscles, in a fish-like swimming body, which causes the body flapping in the transversal direction and create a thrust force to propel the body to cruise in the longitudinal direction. In this method, the fish body is discretized as mass points connected by elastic springs and muscle deformation is critically realized by using a constraint algorithm, called RATTLE, to control relative deformation distances between neighboring mass points of the muscles, while turbulent fluids are treated by a multi-relaxation time lattice Boltzmann method with a large eddy simulation. A validation for the MDM is extensively conducted by comparing our simulation results with the existing experimental and theoretical results. Subsequently, the frequency, amplitude, and wavelength of lengthening of muscles and the stiffness and mass density of the body are systematically varied at different levels and their effects on flapping and cruising motion and flow structures are studied at different Reynolds numbers.

Individual drops are suitable tools to study the liquid-fluid interfacial properties. In this work, forcedisplacement equation and non-linear oscillations of a pendent drop are numerically investigated. The presented novel force-displacement function allows following the dynamics of a pendent drop and realizing its elastic behavior. The growth and detachment of drop, which is pending due to gravity from a capillary tip, is considered (assuming high density and high viscosity ratios and immiscible two-phase flows). Twodimensional multi-relaxation time lattice Boltzmann method (MRT-LBM) was used to simulate growth, detachment, and oscillations of the drop using a conservative model for high-density ratio. The forcedisplacement function of a pendent drop (FDFPD), which is non-linear, was introduced. Using FDFPD, the non-linear elastic specifications of the pendent drop were determined. It was realized that the drop shows three different elastic behaviors simultaneously (hardening, linear, and softening). The drop superharmonic and subharmonic frequencies were calculated, using the natural frequency of the linear portion of FDFPD. Besides, the drop would grow as long as its displacement is between the extrema of FDFPD. In addition, a dynamic criterion for the onset of detachment was established. Also, increasing the Bond number from 0.11 to 1.96, while keeping Reynolds number equal to 0.023, accelerates the drop detachment and increases the linear portion of FDFPD. It was shown that increasing Capillary number from 1.8E-5 to 7.3E-4, while keeping Reynolds number equal to 0.023, accelerates the drop detachment and increases the non-linear portions of FDFPD.

Multi relaxation time Lattice Boltzmann analysis of lid-driven rectangular cavity subject to various obstacle configurations

For a regional land subsidence problem, there are difficulties for the traditional finite element method to solve the regional groundwater flow equation involved. A new finite element method - multiscale finite element method (MsFEM) applied to resolve three dimensional groundwater flow problem- is introduced. Three advantages make the MsFEM very useful for groundwater flow simulation in a large region with highly heterogeneous porous media. One advantage is that this method can significantly save computing efforts by coarse grid mesh. The variation of parameters in an element is brought to the multiscale base functions. Second one is that this method can to a large extent avoid large aspect ratios of elements by combining aquifers and aquitards in one element. The third advantage is that the hydraulic heads in different depths of aquitards or aquifers could be rather accurately interpolated using the multiscale base functions and the nodal heads of the element by MsFEM. The third advantage is useful for the subsidence modeling. A numerical example is done to verify the advantages of MsFEM. Finally, the MsFEM is applied to solve the regional land subsidence model of Shanghai, which includes a three-dimensional groundwater flow mathematical model and a one-dimensional subsidence model. The traditional two-step approach is followed in this study, with the hydrodynamics of the pumped multiaquifer system first simulated by a 3-D groundwater flow model and the subsidence then computed with a 1-D subsidence model with the pore pressure field specified as an external distributed source of strength within the porous medium. The simulation period is from March, 1986 to December, 1998. Using MsFEM, the aquifer system in Shanghai is divided into six layers, which means one aquifer and one aquitard are in one layer with an average thickness of about 50 meters. Every element in MsFEM is subdivided into 7 sub-layers in the vertical direction and every horizontal layer in an element is divided into 4 hexahedral elements. So each element is subdivided into 28 hexahedral sub-cells, which allows the heterogeneity of aquifers and aquitards to be considered by multiscale base functions. The aquifers system in total is discretized into 19,996 elements with a total of 25,000 nodes. The hydraulic heads in any depth of aquitards or aquifers could be interpolated using the multiscale base functions and the nodal heads of the element. It is very useful for the settlement calculation for the aquitards or aquifers after hydraulic heads at nodes of elements are obtained by MsFEM. The application of MsFEM significantly saves computing efforts, effectively decreases the aspect ratios of elements and obtains good results, which proves the MsFEM can be applied to solve the real regional 3D groundwater flow problems, and it is an effective numerical method for regional land subsidence modeling.

A Three-Dimensional Finite Element - Finite Difference Model for Simulating Confined and Unconfined Groundwater Flow

Modeling the movement of hazardous waste in groundwater was identified by the US Department of Energy (DOE) as one of the grand challenges in scientific computation. In recognition of this need, DOE has provided support for a group of scientists from several national laboratories and universities to conduct research and development in groundwater flow and contaminant transport modeling. This group is part of a larger consortium of researchers, collectively referred to as the Partnership in Computational Science (PICS), that has been charged with the task of applying high-performance computational tools and techniques to grand challenge areas identified by DOE. One of the goals of the PICS Groundwater Group is to develop a new three-dimensional groundwater flow and transport code that is optimized for massively parallel computers. An existing groundwater flow code, 3DFEMWATER, was parallelized in order to serve as a benchmark for these new models. The application of P-FEM, the parallelized version of 3DFEMWATER, to a real field site is the subject of this report.

This report extends verification and validation testing of the NUFT package of codes (Nitao 2000a,b) to the US1P module of code designed for simulation of single-phase mixed or “coupled” saturated and unsaturated (or “variably saturated”) groundwater flow. Importantly, the verification and validation testing of US1P in this report includes performance evaluation of a modified numerical algorithm that was not included in prior quality assurance (QA) of the NUFT package by Carle et al. (2014) for Underground Test Area (UGTA) project activities, which are directed at assessment of radionuclide contamination in groundwater sourced from underground nuclear test locations at the Nevada National Security Site (NNSS). An immediate purpose of this report is to provide QA for ongoing large-scale, three-dimensional (3-D) groundwater flow modeling of transient water levels associated with longterm water supply pumping and underground nuclear testing at the NNSS (Jackson and Fenelon, 2018; Jackson et al., 2021). For UGTA activities, the QA refers to the standards of ASTM (1996) for verification and validation testing of groundwater modeling codes.

Modeling Three-Dimensional Groundwater Flow and Advective Contaminant Transport at a Heterogeneous Mountainous Site in Support of Remediation Strategy Quanlin Zhou, Jens T. Birkholzer, Iraj Javandel, and Preston D. Jordan Ernest Orlando Lawrence Berkeley National Laboratory Earth Sciences Division 1 Cyclotron Road, MS 90-1116, Berkeley CA 94720 USA Abstract A calibrated groundwater flow model for a contaminated site can provide substantial information for assessing and improving hydraulic measures implemented for remediation. A three-dimensional transient groundwater flow model was developed for a contaminated mountainous site, at which interim corrective measures were initiated to limit further spreading of contaminants. This flow model accounts for complex geologic units that vary considerably in thickness, slope, and hydrogeologic properties, as well as large seasonal fluctuations of the groundwater table and flow rates. Other significant factors are local recharge from leaking underground storm drains and recharge from steep uphill areas. The zonation method was employed to account for the clustering of high and low hydraulic conductivities measured in a geologic unit. A composite model was used to represent the bulk effect of thin layers of relatively high hydraulic conductivity found within bedrock of otherwise low conductivity. The inverse simulator ITOUGH2 was used to calibrate the model for the distribution of rock properties. The model was initially calibrated using data collected between 1994 and 1996. To check the validity of the model, it was subsequently applied to predicting groundwater level fluctuation and groundwater flux between 1996 and 1998. Comparison of simulated and measured data demonstrated that the model is capable of predicting the complex flow reasonably well. Advective transport was approximated using pathways of particles originating from source areas of the plumes. The advective transport approximation was in good agreement with the trend of contaminant plumes observed over the years. The validated model was then refined to focus on a subsection of the large system. The refined model was subsequently used to assess the efficiency of hydraulic measures implemented for remediation.