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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Project Title: Adaptive Vertical Grid Enhancement for E3SM (Final Technical Report)

During the first phase of the project (2018/05-2021/05), we proved the hypothesis that, without tuning, high vertical resolution improves the representation of unresolved, parameterized low altitude clouds such as stratocumulus clouds in global climate models. We evaluated the effectiveness of the newly developed computational framework, Framework for Improvement by Vertical Enhancement (FIVE) by implementing it into E3SM. FIVE aims to improve representation of the target cloud, low level cloud for this project, with use of a locally high vertical resolution for computation of selected processes. FIVE was assessed via direct comparison among E3SM, E3SM-FIVE, and satellite data as well as a newly developed ensemble artificial neural network methodology. We demonstrated that E3SM-FIVE remarkably improves marine stratocumulus representation. To advance the FIVE methodology, we took a first step toward the adaptive vertical grid in the FIVE method by modifying the E3SM single column model. For future application of FIVE to the global storm resolving model with a few km horizontal grid resolution, we developed the vertical-meridional two-dimensional (2D) Hadley circulation model, which allows one to run simulations with much higher vertical resolution and significantly longer duration than current three-dimensional global storm resolving model. During the second phase of the project (2021/05-2023/11; period for this technical report), we sought a way to appropriately transform FIVE to a regionalized version of FIVE, which allows one to select locations with/without FIVE. In parallel, we demonstrated that E3SM-FIVE with a 25-km mesh significantly reduced the bias associated with coastal stratocumulus. Furthermore, we showed that the same improvement was able to be obtained with the use of both the Regional Refined Model (RRM) targeted to one of the stratocumulus regions with 25-km resolution and FIVE. We explored a new implementation strategy of FIVE with our 2D Hadley circulation model. In parallel we applied the 2D Hadley circulation model to study the double intertropical convergence zone bias with storm resolving model resolution and aerosol-cloud interactions within the Hadley circulation with near large eddy simulation resolution. Last, we have been investigating Arctic mixed-phase stratocumulus clouds with large eddy simulations in order to improve their representation in global models. During the course of the entire project, 6 journal articles were published, and 3 manuscripts are currently in preparation. We gave a total of 30 presentations at various domestic and international conferences. In addition we gave 6 seminar talks at universities and a national laboratory. E3SM- FIVE is available as a branch of E3SM.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2015

Large Eddy Simulation of High-Speed, Premixed Ethylene Combustion

A large-eddy simulation / Reynolds-averaged Navier-Stokes (LES/RANS) methodology is used to simulate premixed ethylene-air combustion in a model scramjet designed for dual mode operation and equipped with a cavity for flameholding. A 22-species reduced mechanism for ethylene-air combustion is employed, and the calculations are performed on a mesh containing 93 million cells. Fuel plumes injected at the isolator entrance are processed by the isolator shock train, yielding a premixed fuel-air mixture at an equivalence ratio of 0.42 at the cavity entrance plane. A premixed flame is anchored within the cavity and propagates toward the opposite wall. Near complete combustion of ethylene is obtained. The combustor is highly dynamic, exhibiting a large-scale oscillation in global heat release and mass flow rate with a period of about 2.8 ms. Maximum heat release occurs when the flame front reaches its most downstream extent, as the flame surface area is larger. Minimum heat release is associated with flame propagation toward the cavity and occurs through a reduction in core flow velocity that is correlated with an upstream movement of the shock train. Reasonable agreement between simulation results and available wall pressure, particle image velocimetry, and OH-PLIF data is obtained, but it is not yet clear whether the system-level oscillations seen in the calculations are actually present in the experiment.

Ramesh, Kiran↗
NASA NTRS1993

A hybrid finite element-boundary integral for the analysis of cavity-backed antennas of arbitrary shape

This is the final report on this project which was concerned with the analysis of cavity-backed antennas and more specifically spiral antennas. The project was a continuation of a previous analysis, which employed rectangular brick elements, and was, thus, restricted to planar rectangular patch antennas. A total of five reports were submitted under this project and we expect that at least four journal papers will result from the research described in these reports. The abstracts of the four previous reports are included. The first of the reports (028918-1-T) is over 75 pages and describes the general formulation using tetrahedral elements and the computer program. Report 028918-2-T was written after the completion of the computer program and reviews the capability of the analysis and associated software for planar circular rectangular patches and for a rectangular planar spiral. Measurements were also done at the University of Michigan and at Mission Research Corp. for the purpose of validating the software. We are pleased to acknowledge a partial support from Mission Research Corp. in carrying out the work described in this report. The third report (028918-3-T) describes the formulation and partial validation (using 2D data) for patch antennas on a circular platform. The 3D validation and development of the formulation for patch antennas on circular platforms is still in progress. The fourth report (028918-4-T) is basically an invited journal paper which will appear in the 'J. Electromagnetic Waves and Applications' in early 1994. It describes the application of the finite element method in electromagnetics and is primarily based on our work here at U-M. This final report describes the culmination of our efforts in characterizing complex cavity-backed antennas on planar platforms. The report describes for the first time the analysis of non-planar spirals and non-rectangular slot antennas as well as traditional planar patch antennas. The comparisons between measurements and calculations are truly impressive. Another unique aspect of this work is the incorporation of the FFT as part of the BiCG solver by overlaying a structured triangular mesh over the unstructured mesh. The implementation of this BiCG-FFT solution algorithm is important in minimizing the CPU and storage requirements. This final report will be submitted for publication in a refereed journal.

Gong, Jian↗
DOE OSTI2016

The application of MAMMOTH for a detailed tightly coupled fuel pin simulation with a station blackout

The accurate calculation of desired quantities to predict fuel behavior in a nuclear reactor requires the solution of inter linked equations representing different physics phenomena. Traditional fuels performance codes often rely on internal empirical models for the pin power density and a simplified boundary condition on the cladding outer surface. These simplifications are performed because of the difficulty of coupling applications or codes on differing domains and mapping the required data. In this work the MAMMOTH application is employed in the demonstration of an approach that more consistent with first principles, in a simulation that couples the neutronics application Rattlesnake, the thermal fluids application RELAP-7 and the fuels performance application BISON. A single fuel pin was modeled based on the dimensions of a fuel rod from a Westinghouse 17*17 optimized PWR fuel assembly. The simulation consisted of a depletion period of 1343 days, representing three full operating cycles, followed by a station blackout (SBO) event. The fuel rod was depleted with a total pin power of 65.81 kW. After 1343 days the fission power was reduced to zero (simulating a reactor shutdown). Decay heat calculations provided the time-varying energy source after this time. For this problem, Rattlesnake, BISON, and RELAP-7 are coupled under MAMMOTH in a tightly coupled approach. Each system solves its physics on a separate mesh and, for RELAP-7 and BISON, on only a subset of the full problem domain. Rattlesnake solves the neutronics over the whole domain, which includes the fuel, cladding, gaps, water, and top and bottom rod holders. Here BISON is applied to the fuel and cladding with a 2-D axisymmetric domain, and RELAP-7 is applied to the flow of the circular outer water channel with a set of 1-D flow equations. For this work, the mesh on the Rattlesnake side is either be 3-D (for low order PN transport or diffusion) or 2-D axisymmetric (for diffusion). BISON has a matching ring structure mesh for the fuel so both the power density and local burnup are transferred accurately from Rattlesnake. At each depletion time step, Rattlesnake calculates a power density, fission density rate, burnup distribution and fast flux based on the current water density and fuel temperature. These are then mapped to the BISON mesh to perform a fuels performance solution. BISON calculates the fuel temperature and cladding surface temperature based upon the current power density and bulk fluid temperature. RELAP-7 then calculates the fluid temperature, water density fraction and water phase velocity based upon the cladding surface temperature. The fuel temperature and the fluid density are then passed back to Rattlesnake for another neutronics calculation. For this paper, sets of results from the detailed calculation are provided for both depletion and the SBO event. We demonstrate that a detailed simulation akin to first principles can be achieved using MAMMOTH and the various MOOSE application on differing domains. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1984

Inlet flowfield investigation. Part 2: Computation of the flow about a supercruise forebody at supersonic speeds

A numerical procedure which solves the parabolized Navier-Stokes (PNS) equations on a body fitted mesh was used to compute the flow about the forebody of an advanced tactical supercruise fighter configuration in an effort to explore the use of a PNS method for design of supersonic cruise forebody geometries. Forebody flow fields were computed at Mach numbers of 1.5, 2.0, and 2.5, and at angles-of-attack of 0 deg, 4 deg, and 8 deg. at each Mach number. Computed results are presented at several body stations and include contour plots of Mach number, total pressure, upwash angle, sidewash angle and cross-plane velocity. The computational analysis procedure was found reliable for evaluating forebody flow fields of advanced aircraft configurations for flight conditions where the vortex shed from the wing leading edge is not a dominant flow phenomenon. Static pressure distributions and boundary layer profiles on the forebody and wing were surveyed in a wind tunnel test, and the analytical results are compared to the data. The current status of the parabolized flow flow field code is described along with desirable improvements in the code.

Paynter, G. C.↗
NASA NTRS2018

Implementation of a Matrix Crack Spacing Parameter in a Continuum Damage Mechanics Finite Element Model

Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.

Hyder, Imran↗
DOE OSTI2016

An Overview of Material Models in the BISON Fuel Performance Code

BISON is a modern finite element-based nuclear fuel performance code that has been under development at Idaho National Laboratory (INL) since 2009. The code is applicable to both steady and transient fuel behavior and supports the use of one-, two-, and three-dimensional meshes. BISON is designed to be a multi-fuels code. Although primarily applied to Light Water Reactor (LWR) fuel to date, the code has been used to analyze TRISO-coated particle fuel and metal fuel in rod and plate form, design and interpret fuel irradiation experiments and investigate novel fuel concepts. Nuclear fuel operates in an extreme environment that induces complex multiphysics phenomena occurring over distances ranging from inter-atomic spacing to meters, and times scales ranging from microseconds to years. To simulate this behavior requires a wide variety of material models which are often complex and nonlinear. Nearly all of the material models currently available in BISON are empirical, using correlations from existing fuel performance codes or material property libraries. Although these models perform adequately under many conditions, they have well-understood limitations. One obvious weakness is that the models are only valid in the domain of the associated experimental data, and extrapolating beyond this domain can result in substantial errors. A further weakness is that these models are often correlated in terms of imprecise quantities, such as burnup. Materials can, for example, reach a given burnup under very different circumstances, leading to very different material behavior. To overcome these weaknesses, efforts are underway with BISON to develop models based on a multi-scale approach, where material behavior is described with a series of interdependent microstructure based models. This paper provides an overview of the material models available in BISON. To keep the scope manageable, only LWR fuel will be considered. The first section focuses on UO{sub 2} fuel, identifying the models generally required and briefly describing those that have been implemented in the code. The second section repeats this approach for Zircaloy cladding. A final section provides examples of areas where multi-scale material modeling has been applied to BISON. BISON is a modern 2D and 3D nuclear fuel performance code that is applicable to multiple fuel forms. A wide variety of complex and nonlinear material models are required to simulate fuel behavior. Focusing on UO{sub 2} fuel and Zircaloy cladding (LWR fuel), the set of empirical models currently implemented in BISON have been reviewed. To overcome some of the deficiencies associated with empirical models, multi-scale material models are being developed. Two multi-scale models that have been used in BISON were reviewed. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2020

Filtration Performance Results: Sierra Peaks Material No. 4

Sandia National Laboratories (SNL) assessed the filtration performance of materials from Sierra Peaks to identify alternatives which may perform similarly to materials used in FDA-approved N95 respirators. This work is meant to characterize the aerosol performance of materials to give Sierra Peaks information for them to determine if they elect to submit masks made using these materials for follow-on N95 certification testing at an accredited facility. The R&D testbed used is a large-scale filtration system designed to test commercial filter boxes. System modifications were performed to simulate, where possible, parameters defined by the National Institute for Occupational Safety and Health (NIOSH) for certification of filter materials for N95 respirators (NIOSH 2019). The system is a pull-through design. Air enters through a Laminar Flow Element (LFE) and the volumetric flow is measured based on the pressure drop across the LFE. Pressure is measured via a Pressure Transducer (PT). The air then passes through a High Efficiency Particulate Air (HEPA) filter to purge the air of ambient airborne particulates. Test aerosol is injected into the flow shortly after and mixing is induced via a coarse mesh. The airflow is allowed to fully develop prior to arriving at the test section. The aerosol then passes through the test material mounted in a box in the test section. Pressure drop across the test article is measured and aerosol sampling probes measure the aerosol concentrations upstream and downstream of the sample. The air passes through a second HEPA filter prior to being exhausted to ambient by a blower. A Topas aerosol generator is used to produce the test aerosol from Sodium Chloride (NaC1) dissolved in deionized (DI) water. Generated aerosol passes through a heated mixing chamber and a desiccant dryer to produce nanosized solid-state particulates. A dilution loop allows for the aerosol concentration to be regulated. The aerosol sampling probes upstream and downstream of the test section are aligned with the flow path. These are ducted directly to the aerosol sizing and counting instruments. A Laser Aerosol Spectrometer (LAS) was used for data collection in the original configuration of the system and was also used for initial testing in this project. Because the lower measurement range for the LAS is 90 nanometers (nm), the LAS was switched out for a more complicated Scanning Mobility Particle Sizer (SMPS) spectrometer system. The SMPS is comprised of an Electrostatic Classifier (EC), Differential Mobility Analyzer (DMA), and a Condensation Particle Counter (CPC). This enabled data collection at 75 nm, the particle size called out in the NIOSH guidelines.

36 MATERIALS SCIENCE↗
NASA NTRS2015

Impact and Penetration of Thin Aluminum 2024 Flat Panels at Oblique Angles of Incidence

The U.S. Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) are actively involved in improving the predictive capabilities of transient finite element computational methods for application to safety issues involving unintended impacts on aircraft and aircraft engine structures. One aspect of this work involves the development of an improved deformation and failure model for metallic materials, known as the Tabulated Johnson-Cook model, or MAT224, which has been implemented in the LS-DYNA commercial transient finite element analysis code (LSTC Corp., Livermore, CA) (Ref. 1). In this model the yield stress is a function of strain, strain rate and temperature and the plastic failure strain is a function of the state of stress, temperature and strain rate. The failure criterion is based on the accumulation of plastic strain in an element. The model also incorporates a regularization scheme to account for the dependency of plastic failure strain on mesh size. For a given material the model requires a significant amount of testing to determine the yield stress and failure strain as a function of the three-dimensional state of stress, strain rate and temperature. In addition, experiments are required to validate the model. Currently the model has been developed for Aluminum 2024 and validated against a series of ballistic impact tests on flat plates of various thicknesses (Refs. 1 to 3). Full development of the model for Titanium 6Al-4V is being completed, and mechanical testing for Inconel 718 has begun. The validation testing for the models involves ballistic impact tests using cylindrical projectiles impacting flat plates at a normal incidence (Ref. 2). By varying the thickness of the plates, different stress states and resulting failure modes are induced, providing a range of conditions over which the model can be validated. The objective of the study reported here was to provide experimental data to evaluate the model under more extreme conditions, using a projectile with a more complex shape and sharp contacts, impacting flat panels at oblique angles of incidence.

Ruggeri, Charles R.↗
DOE OSTI2021

A linked-scale coupled model of mass erosion and redistribution in plasma-exposed micro-foam surfaces

Surface evolution due to exposure to harsh environments is of importance in many scientific and technological applications. In plasma-exposed materials, the surface receives charged particles from the plasma, leading to a series of processes that drive the system far from equilibrium and may lead to the severe deterioration of the surface properties. Although surface morphological changes are driven by atomic collisions taking place over picoseconds and nanometers, these processes result in mass loss and redistribution of matter over much larger length and time scales. This necessitates a multi-scale approach capable of capturing the range of processes linking primary atomic collision events with engineering-level surface geometry changes. In this paper, we develop a computational model to simulate the morphological evolution and effective erosion rate of micro-architected tungsten foams during low-energy plasma ion bombardment. Furthermore, the model acts on several length scales, with the energy and angular dependence of the sputtering yield of flat tungsten surfaces determined using the SRIM code based on the binary collision approximation. This information is introduced into a low-fluence, short-term Monte Carlo raytracing model, and further into a high-fluence, long-term particle transport model. In the latter, material particles representing billions of atoms are described in a digitized 3-D representation of the foam structure from X-ray tomography data, and are sputtered off and redeposited using the atomistic information. We show that the redeposition of sputtered atoms leads to partial self-healing in the bottom layers with a sharp reduction in the sputtering coefficient of low density foams, roughly 25% of the solid W value. This is in qualitative agreement with recent experiments on low porosity W structures. At high fluence, the foam structure degrades considerably as there are fewer ligaments available to recapture sputtered atoms and, consequently, the sputtering rate increases again.

36 MATERIALS SCIENCE↗
DOE OSTI2017

An Experimental and Numerical Study of Diesel Spray Impingement on a Flat Plate

Combustion systems with advanced injection strategies have been extensively studied, but there still exists a significant fundamental knowledge gap on fuel spray interactions with the piston surface and chamber walls. This paper is meant to provide detailed data on spray-wall impingement physics and support the spray-wall model development. The experimental work of spray-wall impingement with non-vaporizing spray characterization, was carried out in a high pressure-temperature constant-volume combustion vessel. The simultaneous Mie scattering of liquid spray and schlieren of liquid and vapor spray were carried out. Diesel fuel was injected at a pressure of 1500 bar into ambient gas at a density of 22.8 kg/m3 with isothermal conditions (fuel, ambient, and plate temperatures of 423 K). A Lagrangian-Eulerian modeling approach was employed to characterize the spray-gas and spray-wall interactions in the CONVERGE framework by means of a Reynolds-Averaged Navier-Stokes (RANS) formulation. A set of turbulence and spray break-up model constants was identified to properly match the aforementioned measurements of liquid penetration within their experimental confidence intervals. An accuracy study on varying the minimum mesh size was also performed to ensure the grid convergence of the numerical results. Experimentally validated computational fluid dynamics (CFD) simulations were then used to investigate the local spray characteristics in the vicinity of the wall with a particular focus on Sauter Mean Diameter (SMD) and Reynolds and Weber numbers. The analysis was performed by considering before- and after-impingement conditions in order to take in account the influence of the impinged wall on the spray morphology.

42 ENGINEERING↗
DOE OSTI2014

Methodological Aspects of Shielding and Activation Analyses for ITER Diagnostics Systems - Paper 125

It is expected that the diagnostics systems of the ITER tokamak will provide valuable measurement data about the first in its kind D-T fusion plasma with emission of 14 MeV neutrons. These systems must withstand the neutron and secondary photon radiation along the ITER operation. Under the neutron irradiation the ITER materials are getting radioactive and therefore an adequate shielding must be provided along all the time of ITER operation and shut-down for the reliable machine operation and for the safe personnel access to its components, such as the diagnostics ports. These are the prerequisites for the shielding and activation analysis of the ITER diagnostics systems discussed in this paper. This paper provides insight into the current tasks of neutronics support for the development of ITER diagnostics systems. The tasks themselves range from relatively straightforward ones such as Monte Carlo radiation transport calculations for shielding analyses of the diagnostics systems, to more advanced tasks of Shut-Down Dose Rate (SDDR) analyses for which the dedicated Rigorous 2-Step mesh-based (R2Smesh) and Direct 1-Step (D1S) methodologies were applied. The accuracy and precision of the ITER neutronics analysis is dependent on the methodological approaches and the implying modeling assumptions. In addition to the SDDR challenges, another distinguishing feature of fusion neutronics is a wide use of CAD-based neutronics modeling to design components of fusion devices such as ITER and DEMO. Basically, there are two possibilities of CAD geometry settings in Monte Carlo (MC) radiation transport models, either by the geometry format conversion of CAD models into the format of MC models by means of the interface programs such as McCad and MCAM or by the direct use of CAD geometry engine in MC calculations such as it was realized in the DAGMC code approach. Several conversion interfaces and the DAGMC software library have been tested on the 3D ITER model developed for the CAD-MCNP benchmark. It was concluded that the considered approaches have reached the maturity level to allow their application to real ITER design analyses.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗
DOE OSTI2025

Hydrodynamic expansion and near-infrared absorption of x-ray heated aluminum plasmas

We use x-ray pulses from dense argon plasmas at the Z Machine (Sandia National Laboratories) to generate hypersonic aluminum plasmas akin to material ejecta during proposed planetary defense missions, fusion reactor wall excursions, and other high-energy density processes. Near-infrared absorption is used to diagnose the controlled expansion of the plasmas through cylindrical cavities following their generation from x-ray heating of solid aluminum 7075 alloy. The data are compared to multidimensional radiation hydrodynamics simulations utilizing the ALEGRA multiphysics code, accounting for the dynamics of radiation scattering, material phase change, plasma expansion, thermal re-irradiation, and interactions with the cavity and with the infrared beams. To allow for accurate simulation, density functional theory is used to apply the Hagen–Rubens relation for the far-infrared and is adjoined with a detailed configuration accounting model using the Propaceos code, producing opacities spanning 10 −1 –10 4 eV photon energy for aluminum 7075 alloy, and in comparison with pure aluminum. The model is found to agree with experimental data in the higher-fluence regime when the Hagen–Rubens relation is applied. The ejected material, which is observed to travel up to 55 km/s, is comprised of a strongly ionized, non-LTE plasma front at ∼10 eV temperature followed by a weakly ionized LTE gas at higher density. The present findings lend some confidence to the broad-range equation of state and infrared opacity models for weakly ionized aluminum plasmas while demonstrating an approach to their future refinement, with potential application to astrophysical plasmas and other extreme processes.

Adiabatic process↗
DOE OSTI2023

1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (N u ), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Finally, our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

MAGNETIC FIELDS IN COSMOLOGICAL SIMULATIONS OF DISK GALAXIES

Observationally, magnetic fields reach equipartition with thermal energy and cosmic rays in the interstellar medium of disk galaxies such as the Milky Way. However, thus far cosmological simulations of the formation and evolution of galaxies have usually neglected magnetic fields. We employ the moving-mesh code AREPO to follow for the first time the formation and evolution of a Milky Way-like disk galaxy in its full cosmological context while taking into account magnetic fields. We find that a prescribed tiny magnetic seed field grows exponentially by a small-scale dynamo until it saturates around z = 4 with a magnetic energy of about 10% of the kinetic energy in the center of the galaxy's main progenitor halo. By z = 2, a well-defined gaseous disk forms in which the magnetic field is further amplified by differential rotation, until it saturates at an average field strength of ∼6 μG in the disk plane. In this phase, the magnetic field is transformed from a chaotic small-scale field to an ordered large-scale field coherent on scales comparable to the disk radius. The final magnetic field strength, its radial profile, and the stellar structure of the disk compare well with observational data. A minor merger temporarily increases the magnetic field strength by about a factor of two, before it quickly decays back to its saturation value. Our results are highly insensitive to the initial seed field strength and suggest that the large-scale magnetic field in spiral galaxies can be explained as a result of the cosmic structure formation process.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗
DOE OSTI2014

Simulating the universe(s): from cosmic bubble collisions to cosmological observables with numerical relativity

The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another could provide an important observational signature to test this scenario. We develop and implement an algorithm for accurately computing the cosmological observables arising from bubble collisions directly from the Lagrangian of a single scalar field. We first simulate the collision spacetime by solving Einstein's equations, starting from nucleation and ending at reheating. Taking advantage of the collision's hyperbolic symmetry, the simulations are performed with a 1+1-dimensional fully relativistic code that uses adaptive mesh refinement. We then calculate the comoving curvature perturbation in an open Friedmann-Robertson-Walker universe, which is used to determine the temperature anisotropies of the cosmic microwave background radiation. For a fiducial Lagrangian, the anisotropies are well described by a power law in the cosine of the angular distance from the center of the collision signature. For a given form of the Lagrangian, the resulting observational predictions are inherently statistical due to stochastic elements of the bubble nucleation process. Further uncertainties arise due to our imperfect knowledge about inflationary and pre-recombination physics. We characterize observational predictions by computing the probability distributions over four phenomenological parameters which capture these intrinsic and model uncertainties. This represents the first fully-relativistic set of predictions from an ensemble of scalar field models giving rise to eternal inflation, yielding significant differences from previous non-relativistic approximations. Thus, our results provide a basis for a rigorous confrontation of these theories with cosmological data.

79 ASTRONOMY AND ASTROPHYSICS↗