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At least 469 records · Page 26

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Wind Flow Simulation Around NASA KSC Vehicle Assembly Building

A model of the wind flow conditions around Kennedy Space Center (KSC) Vehicle Assembly Building (VA B) is presented. An incompressible Navier-Stokes flow solver was used to compute the flow field around fixed Launch Complex 39 (LC-39) buildings and structures. The 3-D flow field. including velocity magnitude and velocity vectors, was established to simulate the localized wind speeds and directions at specified locations in and around LC-39 buildings and structures. The results of this study not only help explain the physical phenomena of the flow patterns around LC-39 buildings but also are useful to the Shuttle personnel. Current Operations and Maintenance Requirements and Specifications (OMRS) for vehicle transfer operations are based on empirically derived historical data, and no detailed mathematical analysis of wind conditions around LC-39 structures has ever been accomplished.

Vu, B. T.↗

Whistler Waves Generated by Nongyrotropic and Gyrotropic Electron Beams During Asymmetric Guide Field Reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

magnetic reconnection↗

Simulating Catalysis with Realistic Pellet Geometries Using Mesoflow: A Case Study of Catalytic Propane Dehydrogenation

We present a case study of catalytic propane dehydrogenation with our open-source multiphysics solver, Mesoflow. The solver was developed to simulate reactive flow coupled to heterogeneous catalytic reactions and deactivation in the context of complex, mesoscale geometry. The method leverages cartesian block-structured adaptive mesh refinement to capture realistic catalyst microstructural features acquired directly from X-ray computed tomography data. A kinetic model for propane dehydrogenation and catalyst deactivation was developed based on temporal analysis of products (TAP) reactor experiments. The TAP reactor experiments allow for precise characterization of intrinsic kinetic reaction steps which are implemented into Mesoflow simulations to model the spatial and temporal evolution of reactants, products, and catalyst active sites. The short-term and long-term deactivation behavior is studied by using XCT data collected from fresh and aged catalyst pellets, which exhibit different microstructural features. This study employs time-splitting algorithms to connect disparate reaction and flow timescales, enabling the simulations to achieve realistic deactivation timescales on the order of minutes while the flow time-scales for small particles (100 microns) are several milliseconds. We also introduce a flexible automated python script that writes the necessary files to construct a Mesoflow simulation from user-created chemical mechanisms. We will also introduce a few new features that are added to Mesoflow such as higher order schemes, implicit chemistry integrators and the ability to run on AMD and NVIDIA graphics-processing-units.

AMReX↗

Understanding performance variability in standard and pipelined parallel Krylov solvers

In this work, we collect data from runs of Krylov subspace methods and pipelined Krylov algorithms in an effort to understand and model the impact of machine noise and other sources of variability on performance. We find large variability of Krylov iterations between compute nodes for standard methods that is reduced in pipelined algorithms, directly supporting conjecture, as well as large variation between statistical distributions of runtimes across iterations. Based on these results, we improve upon a previously introduced nondeterministic performance model by allowing iterations to fluctuate over time. We present our data from runs of various Krylov algorithms across multiple platforms as well as our updated non-stationary model that provides good agreement with observations. We also suggest how it can be used as a predictive tool.

97 MATHEMATICS AND COMPUTING↗

Exponential time differencing for the tracer equations appearing in primitive equation ocean models

The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several equations may be added to and coupled to the dynamics system. In many relevant situations, the time-step requirements of explicit methods imposed by the transport and mixing in the vertical direction are more restrictive than those for the horizontal, and this may cause the need to use very small time steps if a fully explicit method is employed. To overcome this issue, we propose an exponential time differencing (ETD) solver where the vertical terms (transport and diffusion) are treated with a matrix exponential, whereas the horizontal terms are dealt with in an explicit way. In this work, we investigate numerically the computational speed-ups that can be obtained over other semi-implicit methods, and we analyze the advantages of the method in the case of multiple tracers.

42 ENGINEERING↗

Efficient and Flexible Sensitivity Matrix Computation for Adaptive Electrical Capacitance Volume Tomography

Electrical capacitance tomography is a widely used sensor modality for flow imaging in many industrial settings. Adaptive Electrical Capacitance Volume Tomography (AECVT) extends the capabilities of traditional ECT by enabling direct volumetric imaging and an improved resolution. Construction of the sensitivity matrix is a necessary step to obtain flow images. This step requires computation of the electric field inside the sensing domain, which is done via a typical field solver such as the finite element method. In this work, we present an efficient and flexible method to construct the sensitivity matrix for Adaptive Electrical Capacitance Volume Tomography (AECVT) based on individual electrode segment excitations and their judicious combination to form desired matrix elements. We illustrate how the proposed method yields the same sensitivity matrix as the traditional method but at a much lower computational cost. Once all segment contributions are obtained, we also indicate how the proposed method, unlike the traditional approach, can generate the sensitivity matrix on demand for an arbitrary combination of synthetic electrodes and obviating the need for any additional field computations. Finally, we present image reconstruction results for two different experimental scenarios where the mutual capacitance data and the corresponding sensitivity vectors are obtained through the proposed measurement combination scheme.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Deterministic Calibration of MFiX-PIC, Part 1: Settling Bed

The Particle-in-cell (PIC) numerical approach for modeling granular solids in fluid flow has gained significant interest in recent years. Valued for its often shorter time-to-solution, the PIC formulation relies on modeling statistical groupings of particles called parcels in cooperation with a solids stress model to affect local solids velocity. This is in contrast to the discrete element model (DEM) where every particle in a system is modelled individually and directly coupled to local solids velocity through Newtonian mechanics. The U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) develops and maintains Multiphase Flow with Interphase eXchanges (MFiX), a collection of open-source computational fluid dynamics (CFD) solvers. Included in the MFiX suite are traditional two-fluid model (TFM) and DEM solvers, and a recently added PIC solver (NETL, 2021). In general, PIC methodologies offer an accuracy trade-off in lieu of computational speed; and therefore, it is important to assess the credibility of MFiX-PIC simulations. For this purpose, a systematic verification, validation and uncertainty quantification (VVUQ) effort was initiated at NETL to assess the new PIC solver

42 ENGINEERING↗

NASA Tech Briefs, July 2013

Dielectrophoresis-Based Particle Sensor Using Nanoelectrode Arrays; Multi-Dimensional Damage Detection for Surfaces and Structures; ULTRA: Underwater Localization for Transit and Reconnaissance Autonomy; Autonomous Cryogenic Leak Detector for Improving Launch Site Operations; Submillimeter Planetary Atmospheric Chemistry Exploration Sounder; Method for Reduction of Silver Biocide Plating on Metal Surfaces; Silicon Micromachined Microlens Array for THz Antennas; Forward-Looking IED Detector Ground Penetrating Radar; Fully Printed, Flexible, Phased Array Antenna for Lunar Surface Communication, Battery Charge Equalizer with Transformer Array; An Efficient, Highly Flexible Multi-Channel Digital Downconverter Architecture; Dimmable Electronic Ballast for a Gas Discharge Lamp; Conductive Carbon Nanotube Inks for Use with Desktop Inkjet Printing Technology; Enhanced Schapery Theory Software Development for Modeling Failure of Fiber-Reinforced Laminates; High-Performance, Low-Temperature-Operating, Long-Lifetime Aerospace Lubricants; Carbon Nanotube Microarrays Grown on Nanoflake Substrates; Differential Muon Tomography to Continuously Monitor Changes in the Composition of Subsurface Fluids; Microgravity Drill and Anchor System; 20 Granular Media-Based Tunable Passive Vibration Suppressor; 21 Miga Aero Actuator and 2D Machined Mechanical Binary Latch; Micro-XRF for In Situ Geological Exploration of Other Planets; Hydrogen-Enhanced Lunar Oxygen Extraction and Storage Using Only Solar Power; Uplift of Ionospheric Oxygen Ions During Extreme Magnetic Storms; Miniaturized, High-Speed, Modulated X-Ray Source; Hollow-Fiber Spacesuit Water Membrane Evaporator 25 High-Power Single-Mode 2.65-micrometers InGaAsSb/AlInGaAsSb Diode Lasers; Optical Device for Converting a Laser Beam Into Two Co-aligned but Oppositely Directed Beams; A Hybrid Fiber/Solid-State Regenerative Amplifier with Tunable Pulse Widths for Satellite Laser Ranging; X-Ray Diffractive Optics; SynGenics Optimization System (SynOptSys); 29 CFD Script for Rapid TPS Damage Assessment; radEq Add-On Module for CFD Solver Loci-CHEM; Science Opportunity Analyzer (SOA) Version 8; 30 Autonomous Byte Stream Randomizer; Distributed Engine Control Empirical/Analytical Verification Tools; Dynamic Server-Based KML Code Generator Method for Level-of-Detail Traversal of Geospatial Data; Automated Planning of Science Products Based on Nadir Overflights and Alerts for Onboard and Ground Processing; Linked Autonomous Interplanetary Satellite Orbit Navigation; Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing; Scheduling Operations for Massive Heterogeneous Clusters; Deepak Condenser Model (DeCoM); Flight Software Math Library; Recirculating 1-K-Pot for Pulse-Tube Cryostats; 35 Method for Processing Lunar Regolith Using Microwaves; Wells for In Situ Extraction of Volatiles from Regolith (WIEVR); and Estimating the Backup Reaction Wheel Orientation Using Reaction Wheel Spin Rates Flight Telemetry from a Spacecraft.

Source record↗

Preliminary Results Cycling GEOS-JEDI with GSI-based Background Errors

The first phase of transitioning the NASA GMAO GEOS atmospheric data assimilation capabilities to JEDI involves the replacement of the Grid-point Statistical Interpolation (GSI) with a corresponding JEDI analysis. This includes taking JEDI's Unified Observation Operator (UFO), its underlying dependencies, and the JEDI solver that enables a hybrid 4DEnVar strategy similar to what is used in the current GEOS-GSI system. Variational analysis involves at least two main components associated with the observation and background cost function terms. The first is directly related to the UFO, which is being carefully validated in a joint collaboration between GMAO and NCEP to demonstrate consistency with corresponding observations usage in GSI. The second component is the background term, which in a hybrid system involves the ability to set up both a climatologically-based term and an ensemble-based term. JEDI provides the means to implement both terms through its BUMP component. Use of BUMP would require a complete re-tune of both climatological and ensemble, which is a non-trivial exercise we would prefer to avoid. As an alternative, the work here studies the results of interfacing the GSI-background error capability (GSIBEC) into JEDI through SABER. With this, the exact same background error covariance formulation used in GSI can be employed in JEDI without need for re-tuning. This brief summary covers the work done to interface GSIBEC into JEDI and shows preliminary results where the background error covariances of the control (GEOS-GSI) and experiment (GEOS-JEDI) are identical in corresponding cycling experiments. The cycling exercise is obviously preliminary and so much can be expected from GEOS-JEDI when compared to GEOS-GSI. There is still a number of features that need closer attention and although in some cases in principle ready to cycle have been intentionally either turned off or not fully exercised (e.g., VarBC is applied but not cycled). Other features are still pending implementation, one such example is the implementation of the Tangent Linear Normal Mode Constraint. Still, results are quite encouraging as hopefully the discussion here illustrates.

Ricardo Todling↗

A Piloted Simulator Evaluation of Transport Aircraft Rudder Pedal Force/Feel Characteristics

A piloted simulation study has been conducted in a fixed-base research simulator to assess the directional handling qualities for various rudder pedal feel characteristics for commercial transport airplanes. That is, the effects of static pedal force at maximum pedal travel, breakout force, and maximum pedal travel on handling qualities were studied. An artificial maneuver with a severe lateral wind shear and requiring runway tracking at an altitude of 50 feet in a crosswind was used to fully exercise the rudder pedals. Twelve active airline pilots voluntarily participated in the study and flew approximately 500 maneuvers. The pilots rated the maneuver performance with various rudder pedal feel characteristics using the Cooper- Harper rating scale. The test matrix had 15 unique combinations of the 3 static pedal feel characteristics. A 10-term, second-order equation for the Cooper-Harper pilot rating as a function of the 3 independent pedal feel parameters was fit to the data. The test matrix utilized a Central Composite Design that is very efficient for fitting an equation of this form. The equation was used to produce contour plots of constant pilot ratings as a function of two of the parameters with the third parameter held constant. These contour plots showed regions of good handling qualities as well as regions of degraded handling qualities. In addition, a numerical equation solver was used to predict the optimum parameter values (those with the lowest pilot rating). Quantitative pilot performance data were also analyzed. This analysis found that the peak values of the cross power spectra of the pedal force and heading angle could be used to quantify the tendency toward directional pilot induced oscillations (PIO). Larger peak values of the cross power spectra were correlated with larger (degraded) Cooper-Harper pilot ratings. Thus, the subjective data (Cooper-Harper pilot ratings) were consistent with the objective data (peak values of the cross power spectra).

Stewart, Eric C.↗

Randomized Preconditioned Solvers for Strong Constraint 4D-Var Data Assimilation

The Strong Constraint 4D Variational (SC-4DVAR) data assimilation method is widely used in climate and weather applications. SC-4DVAR involves solving a minimization problem to compute the maximum a posteriori estimate, which we tackle using the Gauss-Newton method. The computation of the descent direction is expensive since it involves the solution of a large-scale and potentially ill-conditioned linear system, solved using the preconditioned conjugate gradient (PCG) method. Here, to address this cost, we efficiently construct scalable preconditioners using three different randomization techniques, which all rely on a certain low-rank structure involving the Gauss-Newton Hessian. The proposed techniques come with theoretical guarantees on the condition number, and at the same time, are amenable to parallelization. We also develop an adaptive approach to estimate the sketch size and choose between the reuse or recomputation of the preconditioner. We demonstrate the performance and effectiveness of our methodology on two representative model problems—the Burgers and barotropic vorticity equation—showing a drastic reduction in both the number of PCG iterations and the number of Gauss-Newton Hessian products after including the preconditioner construction cost.

Gauss-Newton↗

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Nark, Douglas M.↗

Three-dimensional Skyrme Hartree-Fock-Bogoliubov solver in coordinate-space representation

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform. To remedy the problems with pairing collapse, we implemented the soft energy cutoff and pairing annealing. The convergence of HFB solutions was improved by a sub-iteration method. The Hermiticity violation of differential operators brought by Fourier-transform-based differentiation has also been solved. Furthermore, the accuracy and performance of HFBFFT were tested by benchmarking it against other HFB codes, both spherical and deformed, for a set of nuclei, both well-bound and weakly-bound.

3D coordinate-space representation↗

Predicting extreme anisotropy and shape variations in impact testing of tantalum single crystals

We report recent Taylor cylinder impact tests carried out for Ta single crystals showed strong variations in dimensional changes for different crystallographic directions aligned with the cylindrical axis. In order to capture the effect of crystallography on the deformation characteristics and final shapes of the impacted cylinders, a single crystal material subroutine is adapted and embedded in the solid mechanics/dynamics Finite Element solver Abaqus to simulate the aforementioned single crystal Ta Taylor impact experiments. Details of the coupled model implementation, and insights on the role played by single crystal anisotropic flow on the deformation behavior across a broad range of strain rates and temperatures for different single crystal orientations are presented and discussed. We demonstrate the predictive capability of the adopted crystal plasticity model to capture the significant role played by crystal orientation-induced anisotropy, as well as strain hardening and adiabatic heating, on the dynamic deformation response of crystalline materials. This re-emphasizes the need of microstructure-aware models to improve the accuracy of simulations for high-consequence engineering design.

36 MATERIALS SCIENCE↗

Charge collected by diffusion from an ion track under mixed boundary conditions

Charge-carrier diffusion from an ion track in a silicon substrate at least a few hundred microns thick is analyzed. The substrate upper surface is treated as reflective except for a small section, intended to represent a reverse-biased junction, which is treated as a sink. Total charge collected by the sink is calculated by assuming transport to be governed by an ambipolar diffusion equation with temporally constant and spatially uniform carrier lifetime and diffusion coefficient. Present results apply to a normally incident track but could easily be generalized to arbitrary track direction. The collected charge is found to depend on track length and on the electrostatic capacitance, rather than the area, of the sink. Theoretical predictions are compared to the results of a numerical simulation called the Poisson and Continuity Equation Solver (PISCES) for three cases and are found to agree within a factor of two in the worst case.

Edmonds, Larry D.↗

A solution-adaptive mesh algorithm for dynamic/static refinement of two and three dimensional grids

An adaptive grid algorithm has been developed in two and three dimensions that can be used dynamically with a solver or as part of a grid refinement process. The algorithm employs a transformation from the Cartesian coordinate system to a general coordinate space, which is defined as a parallelepiped in three dimensions. A weighting function, independent for each coordinate direction, is developed that will provide the desired refinement criteria in regions of high solution gradient. The adaptation is performed in the general coordinate space and the new grid locations are returned to the Cartesian space via a simple, one-step inverse mapping. The algorithm for relocation of the mesh points in the parametric space is based on the center of mass for distributed weights. Dynamic solution-adaptive results are presented for laminar flows in two and three dimensions.

Benson, Rusty A.↗