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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Combustion Instabilities Modeled

NASA Lewis Research Center's Advanced Controls and Dynamics Technology Branch is investigating active control strategies to mitigate or eliminate the combustion instabilities prevalent in lean-burning, low-emission combustors. These instabilities result from coupling between the heat-release mechanisms of the burning process and the acoustic flow field of the combustor. Control design and implementation require a simulation capability that is both fast and accurate. It must capture the essential physics of the system, yet be as simple as possible. A quasi-one-dimensional, computational fluid dynamics (CFD) based simulation has been developed which may meet these requirements. The Euler equations of mass, momentum, and energy have been used, along with a single reactive species transport equation to simulate coupled thermoacoustic oscillations. A very simple numerical integration scheme was chosen to reduce computing time. Robust boundary condition procedures were incorporated to simulate various flow conditions (e.g., valves, open ends, and choked inflow) as well as to accommodate flow reversals that may arise during large flow-field oscillations. The accompanying figure shows a sample simulation result. A combustor with an open inlet, a choked outlet, and a large constriction approximately two thirds of the way down the length is shown. The middle plot shows normalized, time-averaged distributions of the relevant flow quantities, and the bottom plot illustrates the acoustic mode shape of the resulting thermoacoustic oscillation. For this simulation, the limit cycle peak-to-peak pressure fluctuations were 13 percent of the mean. The simulation used 100 numerical cells. The total normalized simulation time was 50 units (approximately 15 oscillations), which took 26 sec on a Sun Ultra2.

Paxson, Daniel E.↗
DOE OSTI2020

Efficient and Robust Dynamic Simulation of Power Systems With Holomorphic Embedding

Dynamic simulation is vitally important in power system analysis, but traditional approaches based on numerical integration over small time steps are time-consuming. Also, the Newton-Raphson method suffers from difficulty in convergence when solving nonlinear algebraic equations. In this paper, we propose a novel dynamic simulation approach based on holomorphic embedding. By obtaining a high-order approximation of system dynamics, it achieves a much larger time step and thus enhances the computational efficiency significantly. In addition, the new approach avoids non-convergence issues in solving algebraic equations, which improves robustness. The approach includes flexible modeling of synchronous generators and controllers, and we propose a method for modeling generator coordinate transformations. The approach is tested on the IEEE 39-bus, 10-generator system and a Polish 2383-bus, 327-generator system. The results demonstrate promising computational efficiency and satisfactory numerical robustness for the analysis of large-scale power systems.

42 ENGINEERING↗
NASA NTRS1992

Numerical investigation of the Earth's rotation during a complete precession cycle

A theory for the long-term rotational motion of the quasi-rigid Earth was constructed by numerical integration. The theory spans 72,000 years centered about 1968 A.D., and provides accurate rotational and positional data for the Earth in the recent past and the near future. The physical model is termed dynamically consistent because developments for the active forces and torques are truncated based solely on their magnitudes regardless of their origin. The model includes all appropriate forces and torques due to the geopotential and tidal effects as well as lunisolar and planetary contributions. The elastic and inelastic deformations due to tidal action were too small to affect the mass properties of the Earth at the truncation level of the model. However, long-term dissipative effects of the tidal forces and torques were not negligible. These considerations gave the model its quasi-rigid characterization. The numerical output provided both rotational and orbital-element data. The data were fitted throughout the 72,000-year range using Chebyshev polynomial series.

Richardson, David L.↗
NASA NTRS2019

Conceptual Design of a Counter-Rotating Fan System for Distributed Boundary Layer Ingesting Propulsion

The present paper details the design of the counter rotating fans for a Turboelectric Distributed Propulsion (TeDP) system. Sixteen propulsors installed in mail-slot-shape nacelles are embedded on an aerodynamically optimized hybrid wing-body configuration. The hybrid-wing/body (HWB) configuration which was previously designed to satisfy the conditions of trim, longitudinally static stability and specific cargo space is employed as the baseline configuration in pursuing an optimal distributed propulsion system. A set of distributed propulsors is conceptually designed and the collective performance is evaluated against the target thrust mandated by the mission requirements. The concept of the distributed propulsion allows the fan pressure ratio to be around 1.27~1.32 for the target thrust. In addition, further splitting of the fan pressure ratio by using the counter-rotating fans for each slot realizes the target pressure ratio with low tip speed. In the distributed propulsion system, the nature of the flow conditions and/or the thickness of the ingested boundary layer may differ and result in different propulsive reaction of each individual propulsor. The optimization is, thus, approached from both the propulsion system and individual propulsor perspectives. An optimal distribution of the thrust and power output is determined by how the system utilizes each passage's propulsive characteristics and its interaction with the airframe. These system level analysis and optimization are conducted using an actuator disk model to account for the propulsion-airframe integration numerically. With respect to the propulsor level, aerodynamic shape optimizations of the fan blades are performed in a sequential multi-objective optimization process for various design objectives, such as mass flow rate condition, fan pressure ratio, efficiency and the exit flow angle of the fan stage by using a genetic algorithm, NSGA-II. The radial chord distribution, and meanline distribution of the rotors are designed on the circumferentially averaged axi-symmetric inlet profiles and tested on the six inlet profiles from six divided sectors to reckon flow distortion. The performances of the counter rotating fans are, thus, evaluated accordingly for obtaining distortion tolerant fan. The performance of the distributed propulsion system is evaluated by two CFD tools, i.e., a multi-stage turbo-machinery CFD code and one propulsion-airframe integration flow solver coupled with a body-force model. The optimized boundary layer ingestion propulsion system of 16 distributed slots not only reaches the system target thrust, but also delivers a close to 20% fuel saving benefit against its counterpart 12 distributed clean inlet propulsion system.

Boundary-Layer-Ingestion Propulsion↗
NASA NTRSDate not supplied

Numerical Modeling of No Vent Filling of a Cryogenic Tank with Thermo-dynamic Vent System Assisted Injector

This paper presents a multi-node finite volume model of No Vent Filling (NVF) of a cryogenic tank with Thermo-dynamic Vent System (TVS) assisted injector, using the Generalized Fluid System Simulation Program (GFSSP), a general purpose flow network code. NVF tests were conducted in a CRYOgenic Orbital Testbed (CRYOTE) tank which was filled by liquid nitrogen using a TVS assisted injector with vent valve closed during the entire filling process. In TVS assisted injector, the liquid flow splits into two streams: one stream is routed to a Joule-Thomson (J-T) orifice where the flow immediately flashes from liquid to vapor or two phase mixture because the downstream to J-T leg is maintained at vacuum level.; the other stream is injected into the tank after being cooled by cold vapor of J-T leg in a heat exchanger. The flow through J-T leg is also used to cool the outer metal matrix of the injector which in turn cools the vapor in the tank ullage. The cooling of vapor in the ullage by cold injector surface reduces ullage pressure that allows liquid to enter and fill the tank. An integrated numerical model of the test set up was developed. The model included the dual lines of TVS assisted injector, tank and tank wall. The tank was discretized into multiple fluid nodes and branches to represent the ullage and liquid nitrogen and multiple solid nodes to represent the tank wall and structure. The heat transfer between solid to fluid was calculated from pool boiling correlations which include film, transition, and nucleate boiling, as well as natural convection during pre- and post-boiling. The model also accounts for the condensation of vapor at ullage-injector interface and when it comes in contact with the liquid spray. The predicted pressure, resident mass, wall temperature in the tank were compared with the test data.

Alok Majumdar↗
NASA NTRS1993

Mapping the stability region of the 3:2 Neptune-Pluto resonance

Pluto and Charon are most likely the remnants of a large number of objects that existed in the Uranus-Neptune region at early epochs of the solar system. Numerical integrations have shown that, in general, such objects were ejected from the planetary region on timescales of approximately 10(exp 7) years after Neptune and Uranus reached their current masses. It is thought that the Pluto-Charon system survived to current times without being dynamically removed in this way because it is trapped in a set of secular and mean motion resonances with Neptune. The best-known Pluto-Neptune orbit coupling is the 3:2 mean motion resonance discovered almost 30 years ago by C. Cohen and E. Hubbard. These workers showed that the resonance angle, delta is equivalent to 3(lambda(sub P)) - 2(lambda(sub N)) - omega-bar(sub P) where omega-bar(sub P) is the longitude of perihelion of the Pluto-Charon system, and lambda(sub N) and lambda(sub P) are the mean longitude of Neptune and Pluto-Charon respectively, librates about 180 deg with an amplitude, A(sub delta), of 76 deg. A numerical simulation project to map out the stability region of the 3:2 resonance is reported. The results of these simulations are important to understanding whether Pluto's long-term heliocentric stability requires only the 3:2 resonance, or whether it instead requires one or more of the other Pluto-Neptune resonances. Our study also has another important application. By investigating stability timescales as a function of orbital elements, we gain insight into the fraction of orbital phase space which the stable 3:2 resonance occupies. This fraction is directly related to the probability that the Pluto-Charon system (and possibly other small bodies) could have been captured into this resonance.

Levison, H. F.↗
DOE OSTI2024

Towards modelling AR Sco: generalized particle dynamics and strong radiation-reaction regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realized the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time-step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform E- and B-fields and a static dipole B-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time-steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand–Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytical Aristotelian Electrodynamics expectations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Supersonic solutions of the solar-wind equations

We re-examine the inviscid solar-wind equations with heat conduction from below, and establish a fundamentally new approach for finding stellar solutions. Although the problem is fourth order, only two independent integration constants can be assigned, since two boundary conditions that are required to specify well-behaved supersonic solutions determine the values of the other two constants. The solar-wind-model of Noble and Scarf are essentially accurate for practical purposes, but in a fundamental sense they are not self-consistent. At the supersonic level, the ratio of thermal energy to gravitational potential, (kTr/GMm)(sub s), must lie in a narrow range, between 0.4375 and about 0.40, to permit well-behaved solutions for ionized hydrogen. For a supersonic solution this ratio uniquely determines the constants A and epsilon, which in turn govern not only the escape flux and the energy flux per particle but also T'(lambda approaches 0), the temperature gradient at infinity. It is very difficult to find solutions by trial and error, without employing T'(0) as a guide to the iteration of A and epsilon, because not only must (kTr/GMm)(sub s) be chosen within the acceptable range but then either A or epsilon must be guessed with phenomenal accuracy. Otherwise the numerical integration of temperature and expansion velocity do not yield acceptable values at infinity.

Chamberlain, Joseph W.↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Pulse Detonation Engine Modeled

Pulse Detonation Engine Technology is currently being investigated at Glenn for both airbreathing and rocket propulsion applications. The potential for both mechanical simplicity and high efficiency due to the inherent near-constant-volume combustion process, may make Pulse Detonation Engines (PDE's) well suited for a number of mission profiles. Assessment of PDE cycles requires a simulation capability that is both fast and accurate. It should capture the essential physics of the system, yet run at speeds that allow parametric analysis. A quasi-one-dimensional, computational-fluid-dynamics-based simulation has been developed that may meet these requirements. The Euler equations of mass, momentum, and energy have been used along with a single reactive species transport equation, and submodels to account for dominant loss mechanisms (e.g., viscous losses, heat transfer, and valving) to successfully simulate PDE cycles. A high-resolution numerical integration scheme was chosen to capture the discontinuities associated with detonation, and robust boundary condition procedures were incorporated to accommodate flow reversals that may arise during a given cycle. The accompanying graphs compare experimentally measured and computed performance over a range of operating conditions for a particular PDE. Experimental data were supplied by Fred Schauer and Jeff Stutrud from the Air Force Research Laboratory at Wright-Patterson AFB and by Royce Bradley from Innovative Scientific Solutions, Inc. The left graph shows thrust and specific impulse, Isp, as functions of equivalence ratio for a PDE cycle in which the tube is completely filled with a detonable hydrogen/air mixture. The right graph shows thrust and specific impulse as functions of the fraction of the tube that is filled with a stoichiometric mixture of hydrogen and air. For both figures, the operating frequency was 16 Hz. The agreement between measured and computed values is quite good, both in terms of trend and magnitude. The error is under 10 percent everywhere except for the thrust value at an equivalence ratio of 0.8 in the left figure, where it is 14 percent. The simulation results shown were made using 200 numerical cells. Each cycle of the engine, approximately 0.06 sec, required 2.0 min of CPU time on a Sun Ultra2. The simulation is currently being used to analyze existing experiments, design new experiments, and predict performance in propulsion concepts where the PDE is a component (e.g., hybrid engines and combined cycles).

Paxson, Daniel E.↗
NASA NTRS1989

A numerical study of hypersonic propulsion/airframe integration problem

A numerical analysis procedure useful in the propulsion-airframe integration problem has been established. Flow around a generic hypersonic vehicle forebody is solved using Parabolized Navier-Stokes equations and Thin Layer Navier-Stokes equations. Forebody cross sectional geometry corresponds to a two-ellipse configuration. Effect of forebody geometry on the flow structure, especially at the engine inlet location, is analyzed.

Narayan, J. R.↗
DOE OSTI2020

An Experimental Feasibility Study on Applying Neutron Tomography to Encapsulated Spent Nuclear Fuel - 20050

Visual inspection makes easier to ensure the integrity and safety of spent nuclear fuel (SNF) than any classical techniques. Various classical techniques have been applied but there are no reliable methods to qualitatively and quantitatively verify spent fuel in dry storage. Thus, the present authors have developed the prototype safeguards apparatus for dry storage employing the array of He-4 gas scintillation detectors (S670E, Arktis Radiation Detectors Ltd., Switzerland), newly designed to simultaneously measure thermal and fast neutrons without any moderators. The S670E detector has a cylindrical shape with a diameter of 52 mm and active length of 600 mm (total length: 875 mm). The detector is filled by He-4 gas with an approximate pressure of 180 bar for fast neutron detection, and its inner wall is coated by Li-6 for thermal neutron detection. The scintillation lights generated via Li-6 nuclear reaction and elastic scattering are collected by 24 SiPMs linearly paired at the center of the detector. The detector delivers a TTL (Transistor-Transistor Logic) output for pulse readout and UART (Universal Asynchronous Receiver Transmitter) for device control. In order to assess feasibility of the apparatus, an experimental system has been designed, built, and optimized via computational studies. Cf-252 neutron sources and linearly arrayed detectors, working as a single detector, were occupied for this study due to the difficulties in working with SNF. The laboratory scale cask (diameter: 0.67 m, height: 1.5 m), minimized by a factor of 10 compared to the actual thickness of a commercial TN-32 cask, was also manufactured. The detector array was designed to rotate the lab-scale cask and obtain 36 image profiles at every 10 degrees. All profiles were aligned in single frame image called a sinogram, and the cross-sectional image was then fabricated by the inverse radon transform algorithm. These experiments have been repeated with different configurations and numbers of sources. Some gamma-ray sources were also measured with neutron sources in order to distinguish between neutron and gamma-ray pulses. Basically, a He-4 detector is designed to run on Linux OS so it is difficult to directly apply to Windows-based equipment widely used in S. Korea. Therefore, a new data acquisition board working on Windows OS was designed and built. The board mainly consists of FPGA (Field Programmable Gate Array) and SoC (System on Chip) for TTL pulse readout, sorting measured data, and transferring data to a user interface. In conclusion, the tomographic system at lab-scale has shown considerable potential to detect a partial or gross defect of encapsulated assemblies in dry storage. Next steps of this study will be to 1) repeatedly carry out experiments to demonstrate scientific reliability and validity, and 2) numerically integrate signals with weight factors to enhance the image quality since the suggested system based on passive interrogation method requires longer measurement time. Finally, the system will apply to a commercial dry storage phased out soon in S. Korea. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRSDate not supplied

Integrated Bosch Process System Models for In-Situ Oxygen and Carbon Production

In-Situ Resource Utilization (ISRU) technology is a vital component to NASA’s mission of a sustainable presence on the Moon and Mars. Local resources can be leveraged to reduce resupply frequency and mass. Elements of the Bosch process, combined with the carbothermal reduction process, can produce oxygen on the lunar surface with minimal consumables. The Bosch process can also produce oxygen on the Martian surface by using the CO 2 -rich environment. Between both systems, adsorption pump, solar thermal energy, carbon formation reactor, and water recovery subsystems are modeled and integrated to create a functional model in MATLAB software. The model is used to simulate performance of the system and reduce mass, power, and volume requirements. This integrated system model provides a tool to scale ISRU technologies for oxygen and carbon production. The MATLAB model is created by developing a system of independent subsystem models that are solved for their quasi-steady state values which can be integrated with respect to time to determine the change in current states. A flexible time stepping method is used to ensure a high level of accuracy during periods of rapid change while still making use of a simple explicit integration method. The flexible time step is calculated for each independent subsystem and the minimum value from those is used as the overall time step. A flexible time step is calculated by dividing a resolution value, or the maximum change per time step, by the variables current rate of change. The maximum value from all points in space is used for subsystem models that contain multiple values. The process is done for every variable that is being monitored in each subsystem and the global minimum is used as that iteration’s timestep. Several assumptions used in the MATLAB model for fluid flow dynamics, such as 1-D gas flow through the sorption pump, are supported by modeling in Ansys Fluent software. The Lunar oxygen production system is outlined in Fig. 1. The carbothermal reduction subsystem uses solar energy to heat a mixture of lunar regolith and carbon powder to produce carbon monoxide. To begin, the carbon monoxide feeds to the modified Bosch subsystem along with hydrogen gas. The reactants then enter the carbon formation reactor where water and carbon powder are produced. Solar thermal energy is used to add energy to the reactor, but waste heat from the carbothermal process is another potential heat source. The water is collected and electrolyzed to produce hydrogen which reenters the Bosch subsystem, and the oxygen is stored for downstream use. The carbon powder is collected and feeds back into the carbothermal subsystem. The Martian oxygen production system uses the full Bosch process and is outlined in Fig 2. A CO 2 adsorption pump thermally cycles to scrub and pressurize CO 2 from the environment. Along with an initial supply of hydrogen, the reactants enter the Reverse Water Gas Shift Reactor (RWGSR) which produces carbon monoxide and water. Carbon monoxide and unreacted hydrogen enter the carbon formation reactor to produce water and carbon powder. The water is collected from both reactors and electrolyzed to reintroduce hydrogen and store oxygen for propellant production or life support. Carbon is removed from the carbon formation reactor and stored. The adsorption pump utilizes rapid cycle temperature swings within a stack of zeolite coated surfaces. The subsystem model solves 1-D quasi-steady conservation laws of the quasi-steady form, shown in Eq. 1, for the gas stream and heat exchange liquid to predict performance parameters such as breakthrough capacity and optimum cycle time. The source term S is used to capture interactions between the fluid flows and the sorbent. A quasi-steady-state scheme is used where no time derivatives appear in the governing equations, except for those in the source terms. This results in an autonomous system, where ∂F/∂x = ƒ(F). The fluxes F are provided at the inlet, and an explicit method is used to solve for the spatial distribution of F. The heat and mass flows to the sorbent are then extracted from the source terms. These flows are numerically integrated to produce a 1-D solution for the system’s state as a function of both time and space. The body of the adsorption pump is separated into two semi-independent models: the heat exchanger fluid flow and gas flow through the zeolite coated surfaces. Both models are solved using the above-described method to find a 1-D solution as a function of space and interact only once a timestep is taken. The interaction point is the sorbent through which all heat transfer between the two models must occur. Sorbent mass adsorption is calculated using the Lagergren model, shown in Eq. 2, where the transfer coefficient, λ D , is found by solving a system of nondimensionalized equations derived by using the heat and mass transfer analogy for transport phenomena. Using Grade 544 Type 13X zeolite as the sorbent material, the equilibrium concentration, θ eq , is calculated using the k-site Langmuir isotherm and fit parameters. Additionally, the enthalpy of adsorption used in the model is computed by interpolation of available data [1]. The subsystem model was validated using the Rapid Cycle Temperature Swing Adsorption (RC-TSA) pump. The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC). The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC).

In situ Resource Utilization↗
DOE OSTI2024

Two-loop mixed QCD-electroweak amplitudes for Z+jet production at the LHC: bosonic corrections

Abstract We present a calculation of the bosonic contribution to the two-loop mixed QCD-electroweak scattering amplitudes forZ-boson production in association with one hard jet at hadron colliders. We employ a method to calculate amplitudes in the ’t Hooft-Veltman scheme that reduces the amount of spurious non-physical information needed at intermediate stages of the computation, to keep the complexity of the calculation under control. We compute all the relevant Feynman integrals numerically using the Auxiliary Mass Flow method. We evaluate the two-loop scattering amplitudes on a two-dimensional grid in the rapidity and transverse momentum of theZboson, which has been designed to yield a reliable numerical sampling of the boosted-Zregion. This result provides an important building block for improving the theoretical modelling of a key background for monojet searches at the LHC.

Physics↗
DOE OSTI2022

Mascon distribution techniques for asteroids and comets

The mass-concentration model is an approach that has been used to model the gravitational fields of irregularly shaped bodies such as asteroids and comets. By this approach, the body is treated as a collection of point masses. The method is conceptually simple, easy to program, valid down to the surface, and capable of modeling arbitrary density heterogeneities. How the mass concentrations are distributed as well as how mass is assigned to these concentrations is, however, nontrivial. These aspects significantly affect the accuracy and efficiency of the gravitational model. In this paper, we frame the distribution process in terms of numerical integration applied to finite volume meshes. We describe a new method using unstructured, curvilinear, finite volume meshes to significantly improve the accuracy of the mass-concentration model. We then compare the accuracy and efficiency of several variations of our distribution technique to those from literature using Asteroid Eros and Bennu as example bodies. Our results show that the mascon model can be as accurate as the analytic polyhedral model at the surface using an equivalent number of computational elements—i.e., mascon to surface facets. We report the improvement in the model’s performance can be mainly attributed to the volume mesh topology while mesh curving can provide modest case-dependent improvements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Furthermore, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

58 GEOSCIENCES↗
DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗