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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Visualization of Two-phase Flow Maldistribution in Brazed Plate Heat Exchangers

Brazed plate heat exchangers (BPHEs) are widely used in refrigeration and HVAC applications, but are susceptible to two-phase flow maldistribution especially when operated as evaporators. Existing visualization approaches are either limited to idealized conditions or suffer from poor optical transparency. This paper presents a novel visualization method in which one edge of a BPHE, parallel to the refrigerant inlet or outlet port, is removed by wire electrical discharge machining and replaced with a flat, transparent plate. The planar geometry allows the use of optically and infrared (IR)-transparent materials, enabling both high-speed videography and IR thermography of the two-phase flow at the channel entrances and exits. Preliminary tests with R134a and R1234ze(Z) at saturation temperatures between 5 °C and 15 °C demonstrate that distinct two-phase flow patterns in the inlet header can be clearly identified and differentiated under realistic operating conditions. Potentials of optical flow analysis of high-speed videos are shown to provide objective, quantitative indicators for flow regime characterization and comparison. IR imaging of the outlet port reveals non-uniform temperature distributions at the channel exits, providing independent evidence of maldistribution across the channel stack. Limitations of IR temperature accuracy due to the spectral properties of the sapphire window are discussed, and directions for improvement are identified.

Hausherr, Carsten [Technical University of Berlin ↗
DOE OSTI2021

Parallel Multigrid in Time and Space for Extreme-Scale Computational Science

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations, which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of programmatic interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Description of Sensor Assignment Optimization Method as Deployed on a Multi-Node Cluster

Data analytic methods are being developed to address the problem of how to assign a sensor set in a nuclear facility such that a requisite level of process monitoring capability is realized and that the sensor set is sufficiently rich to determine the status of the individual sensors with respect to need for calibration. There is an awareness in the nuclear industry that data analytics combined with rich sensor sets represent a means to improve operations and reduce costs. In the industry the calibration problem has been previously approached as an empirical data-driven problem with several methods having been developed. However, the experience of the utilities over the past ten years with these methods indicates that the absence of physics-based information renders the data-driven approach less reliable. Complicating factors such as the inherent variability of operation (both equipment alignment and operating condition) can confound a pure data-driven approach while there are no rigorous guidelines for determining what constitutes an adequate sensor set. The solution under development to overcome these shortcomings supplements the data analytic method with process information in a so-called process-constrained data-analytic approach. Simple balance equations are written for generic components (e.g., mechanical pump, valve, and heat exchanger). These do not require a priori knowledge of process parameters, such as heat transfer coefficients or friction factors. All that is needed on the part of the utility user is to identify the components and how they are connected. This report describes the development of a parallel computing capability for determining the optimal sensor set. The optimal sensor set problem suffers from the curse of dimensionality. Computation time increases exponentially as the size of the system grows. To overcome this difficulty a pre-conditioner algorithm is developed to find an approximate solution close the actual solution. This serves as a seed for the full-blown algorithm and acts to constrain the space that must searched. The optimization algorithms are described and the implementation on a parallel computing platform is described. The application of the method to a use case we are solving in collaboration with our utility partner served to illustrate how the default sensor set in a nuclear plant may not provide sufficient coverage to infer sensor calibration status.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Parallel Infrastructure Modeling and Inversion Module for E4D

Electrical resistivity tomography ERT is a method of imaging the electrical conductivity of the subsurface. Electrical conductivity is a useful metric for understanding the subsurface because it is governed by geomechanical and geochemical properties that drive subsurface systems. ERT works by injecting current into the subsurface across a pair of electrodes, and measuring the corresponding electrical potential response across another pair of electrodes. Many such measurements are strategically taken across an array of electrodes to produce an ERT data set. These data are then processed through a computationally demanding process known as inversion to produce an image of the subsurface conductivity structure that gave rise to the measurements. Data can be inverted to provide 2D images, 3D images, or in the case of time-lapse 3D imaging, 4D images. ERT is generally not well suited for environments with buried electrically conductive infrastructure such as pipes, tanks, or well casings, because these features tend to dominate and degrade ERT images. This reduces or eliminates the utility of ERT imaging where it would otherwise be highly useful for, for example, imaging fluid migration from leaking pipes, imaging soil contamination beneath leaking subsurface tanks, and monitoring contaminant migration in locations with dense network of metal cased monitoring wells. The location and dimension of buried metallic infrastructure is often known. If so, then the effects of the infrastructure can be explicitly modeled within the ERT imaging algorithm, and thereby removed from the corresponding ERT image. However, there are a number of obstacles limiting this application. 1) Metallic infrastructure cannot be accurately modeled with standard codes because of the large contrast in conductivity between the metal and host material. 2) Modeling infrastructure in true dimension requires the computational mesh to be highly refined near the metal inclusions, which increases computational demands. 3) The ERT imaging algorithm requires specialized modifications to accommodate high conductivity inclusions within the computational mesh. The solution to each of these challenges was implemented within E4D (formerly FERM3D), which is a parallel ERT imaging code developed at PNNL (IPID #30249). The infrastructure modeling module implement in E4D uses a method of decoupling the model at the metallic interface(s) boundaries, into several well posed sub-problems (one for each distinct metallic inclusion) that are subsequently solved and recombined to form the global solution. The approach is based on the immersed interface method, with has been applied for similar problems in other fields (e.g. semiconductor industry). Comparisons to analytic solutions have shown the results to be very accurate, addressing item 1 above. The solution is implemented about an unstructured mesh, which enables arbitrary shapes to be efficiently modelled, thereby addressing item 2 above. In addition, the algorithm is written in parallel and shows excellent scalability, which also addresses equation 2 above. Finally, because only the boundaries of metallic inclusions are modeled, there are no high conductivity cells within the modeling mesh, and the problem described by item 3 above is no longer applicable.

Johnson, TimC.↗
DOE OSTI2019

A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling

A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the approximation error and significantly improves efficiency. Moreover, the deferred-compression technique introduces minimal overhead and does not affect parallelism. As a result, the new solver achieves linear computational complexity under mild assumptions and excellent parallel scalability. To demonstrate the performance of the new solver, we focus on applying it to solve sparse linear systems arising from ice sheet modeling. The strong anisotropic phenomena associated with the thin structure of ice sheets creates serious challenges for existing solvers. To address the anisotropy, we additionally developed a customized partitioning scheme for the solver, which captures the strong-coupling direction accurately. In general, the partitioning can be computed algebraically with existing software packages, and thus the new solver is generalizable for solving other sparse linear systems. Our results show that ice sheet problems of about 300 million degrees of freedom have been solved in just a few minutes using a thousand processors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Methodology for the Simulation of Molecular Motors at Different Scales

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors—proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

Chemistry↗
DOE OSTI2021

Linear delta systems, hexapod systems, and related methods

A linear delta system includes a support frame, rails mounted to the support frame, linear actuators, each linear actuator configured to translate along a longitudinal length of a respective rail, pairs of parallel rods each coupled to the linear actuators, a platform coupled to a longitudinal end of each of the pairs of parallel rods opposite the respective linear actuator, and an object coupled to the platform. Longitudinal axes of the rails are oriented parallel to each other and lie within a common plane or an uncommon plane. A method of forming a linear delta system includes mounting rails to a support frame, the rails having longitudinal axes that are parallel to each other and lying within a common plane, coupling a linear actuator to each of the rails, coupling a pair of parallel rods to each linear actuator, and coupling a platform to the pairs of parallel rods.

Crawford, Anthony L.↗
DOE OSTI2020

Parallel Time Integration for Constrained Optimization

The number of transistors in an average processor continues to increase, but individual clock speeds have plateaued. Those transistors are instead going into additional cores, increasing the number of different things that a processor can do at once and placing an emphasis on parallel computation. Many problems in scientific computing follow a time-evolution model, and it can be difficult to solve such problems in parallel across the temporal domain. The Multi-Grid Reduction In Time (MGRIT) algorithm, developed at Lawrence Livermore National Laboratory (LLNL), solves differential equations with a method designed specifically to take advantage of extreme numbers of processors by parallelizing across time. The Tri-diagonal MGRIT (TriMGRIT) algorithm, also developed at LLNL, is a generalization of MGRIT which enables parallel-in-time solving of a greater number of problems. Constrained optimization problems, in particular, may be solved in parallel using TriMGRIT. These consist of choosing a control function such that an objective functional is minimized, constrained by a differential-equation. We consider two such problems: applying torque to a pendulum to bring it to a gentle stop and moving a crowd of people from one distribution into another. We also perform some miscellaneous theoretical and practical research, including investigating the use of a line-search subroutine to refine intermediate TriMGRIT results and preliminary work on strategies for choosing operators for TriMGRIT to use.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Bulk heterojunction organic photovoltaic cells made by glancing angle deposition

A method of making a bulk heterojunction organic photovoltaic cell by glancing angle deposition. As the disclosed method relies on a trajectory of incident vapor flux that is not parallel to the substrate normal, micro and nano-scale columnar structures of thin films can be grown on the substrate. There is also disclosed a method of forming a donor-acceptor heterojunction by depositing at least one additional organic material over the columnar structures.

Forrest, Stephen R.↗
DOE OSTI2017

Decentralized Interleaving of Paralleled Dc-Dc Buck Converters

We present a decentralized control strategy that yields switch interleaving among parallel-connected dc-dc buck converters. The proposed method is based on the digital implementation of the dynamics of a nonlinear oscillator circuit as the controller. Each controller is fully decentralized, i.e., it only requires the locally measured output current to synthesize the pulse width modulation (PWM) carrier waveform and no communication between different controllers is needed. By virtue of the intrinsic electrical coupling between converters, the nonlinear oscillator-based controllers converge to an interleaved state with uniform phase-spacing across PWM carriers. To the knowledge of the authors, this work presents the first fully decentralized strategy for switch interleaving in paralleled dc-dc buck converters.

14 SOLAR ENERGY↗
DOE OSTI2015

Exploring Memory Hierarchy to Improve Scientific Data Read Performance, In: 2015 IEEE International Conference on Cluster Computing

Improving read performance is one of the major challenges with speeding up scientific data analytic applications. Utilizing the memory hierarchy is one major line of researches to address the read performance bottleneck. Related methods usually combine solide-state-drives(SSDs) with dynamic random-access memory(DRAM) and/or parallel file system(PFS) to mitigate the speed and space gap between DRAM and PFS. However, these methods are unable to handle key performance issues plaguing SSDs, namely read contention that may cause up to 50% performance reduction. In this paper, we propose a framework that exploits the memory hierarchy resource to address the read contention issues involved with SSDs. The framework employs a general purpose online read algorithm that able to detect and utilize memory hierarchy resource to relieve the problem. To maintain a near optimal operating environment for SSDs, the framework is able to orchastrate data chunks across different memory layers to facilitate the read algorithm. Compared to existing tools, our framework achieves up to 50% read performance improvement when tested on datasets from real-world scientific simulations.

Computer Science↗
DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗
DOE OSTI2020

Protein Molecular Dynamics Simulations with Approximate QM: What Can We Learn?

Classical force fields are essential for computer simulations of proteins and are typically parameterized to reproduce secondary and tertiary structure of isolated proteins. However, while protein-protein interactions are ubiquitous in nature, they are not considered in parameterization efforts and are far less understood than isolated proteins. A better characterization of intermolecular interactions is widely recognized as a key to revolutionizing drug and therapeutic developments with high-throughput computational screening. Urgently needed is a critical assessment of the performance of modern protein force fields against first-principles electronic structure methods and experiments. In a daring step toward this goal, we here describe a comparison of peptide folding dynamics as predicted by a molecular mechanics force field on the one hand and by an approximate electronic structure quantum mechanical (QM) method based on density-functional tight-binding (DFTB) on the other. We further compare the dynamics from straightforward DFTB simulations with a near-linear scaling version of DFTB for massively parallel computation based on the fragment molecular orbital (FMO-DFTB) method. We illustrate differences between the phenomenology of the folding dynamics from these three methods for a small model peptide, as well as charge polarization and dynamic fluctuations, point out possible correlations and implications for force field developers, and discuss the lessons learned that might become applicable to future predictive high-throughput computer screening for personalized neoantigen cancer therapy.

Irle, Stephan↗
DOE OSTI2017

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge–Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming the resulting linear system of equations, one can obtain a method which is much less computationally expensive than the untransformed formulation, and which compares competitively with other time-integration schemes, such as diagonally implicit Runge–Kutta (DIRK) methods. We develop and test several ILU-based preconditioners effective for these large systems. We additionally employ a parallel-in-time strategy to compute the Runge–Kutta stages simultaneously. Numerical experiments are performed on the Navier–Stokes equations using Euler vortex and 2D and 3D NACA airfoil test cases in serial and in parallel settings. In conclusion, the fully implicit Radau IIA Runge–Kutta methods compare favorably with equal-order DIRK methods in terms of accuracy, number of GMRES iterations, number of matrix–vector multiplications, and wall-clock time, for a wide range of time steps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Alternative modeling methods for plasma-based Rf ion sources

Rf-driven ion sources for accelerators and many industrial applications benefit from detailed numerical modeling and simulation of plasma characteristics. For instance, modeling of the Spallation Neutron Source (SNS) internal antenna H{sup −} source has indicated that a large plasma velocity is induced near bends in the antenna where structural failures are often observed. This could lead to improved designs and ion source performance based on simulation and modeling. However, there are significant separations of time and spatial scales inherent to Rf-driven plasma ion sources, which makes it difficult to model ion sources with explicit, kinetic Particle-In-Cell (PIC) simulation codes. In particular, if both electron and ion motions are to be explicitly modeled, then the simulation time step must be very small, and total simulation times must be large enough to capture the evolution of the plasma ions, as well as extending over many Rf periods. Additional physics processes such as plasma chemistry and surface effects such as secondary electron emission increase the computational requirements in such a way that even fully parallel explicit PIC models cannot be used. One alternative method is to develop fluid-based codes coupled with electromagnetics in order to model ion sources. Time-domain fluid models can simulate plasma evolution, plasma chemistry, and surface physics models with reasonable computational resources by not explicitly resolving electron motions, which thereby leads to an increase in the time step. This is achieved by solving fluid motions coupled with electromagnetics using reduced-physics models, such as single-temperature magnetohydrodynamics (MHD), extended, gas dynamic, and Hall MHD, and two-fluid MHD models. We show recent results on modeling the internal antenna H{sup −} ion source for the SNS at Oak Ridge National Laboratory using the fluid plasma modeling code USim. We compare demonstrate plasma temperature equilibration in two-temperature MHD models for the SNS source and present simulation results demonstrating plasma evolution over many Rf periods for different plasma temperatures. We perform the calculations in parallel, on unstructured meshes, using finite-volume solvers in order to obtain results in reasonable time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗