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At least 433 records · Page 24

Computational Issues Associated with Temporally Deforming Geometries Such as Thrust Vectoring Nozzles

During the past decade, computational simulation of fluid flow around complex configurations has progressed significantly and many notable successes have been reported, however, unsteady time-dependent solutions are not easily obtainable. The present effort involves unsteady time dependent simulation of temporally deforming geometries. Grid generation for a complex configuration can be a time consuming process and temporally varying geometries necessitate the regeneration of such grids for every time step. Traditional grid generation techniques have been tried and demonstrated to be inadequate to such simulations. Non-Uniform Rational B-splines (NURBS) based techniques provide a compact and accurate representation of the geometry. This definition can be coupled with a distribution mesh for a user defined spacing. The present method greatly reduces cpu requirements for time dependent remeshing, facilitating the simulation of more complex unsteady problems. A thrust vectoring nozzle has been chosen to demonstrate the capability as it is of current interest in the aerospace industry for better maneuverability of fighter aircraft in close combat and in post stall regimes. This current effort is the first step towards multidisciplinary design optimization which involves coupling the aerodynamic heat transfer and structural analysis techniques. Applications include simulation of temporally deforming bodies and aeroelastic problems.

Boyalakuntla, Kishore↗

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Kreider, Kevin L.↗

Gravity Induced Formation of Concentration Gradients in Supersaturated Binary Solutions

Experimental and theoretical studies of the formation of solute concentration gradient in supersaturated binary solutions in a gravitational field were carried out. The formation of solute concentration gradient was associated with the gravity induced redistribution of subcritical solute clusters. The birth-death process of the new solute-rich phase domains (subcritical solute clusters) was described in terms of the time-dependent Ginzburg Landau model developed for metastable state relaxation in binary (solute + solvent) non-critical solutions in the presence of a gravitational field. A new mathematical Ansatz was developed for solution of the model equations. This Ansatz has allowed to approach for the first time the following important problems: (1) Microstructure of solute distribution inside of the subcritical solute clusters. The analytical results obtained demonstrate that solute inside of the subcritical solute clusters is heterogeneously distributed with a spatially periodic structure. (2) Macrostructure of the solute subcritical clusters distribution in a gravitational field. The subcritical solute clusters are found to be distributed heterogeneously in a gravitational field. This heterogeneity, which is due to the heterogeneous birth-death process of the subcritical solute clusters in a gravitational field, initiates a noticeable solute concentration gradient in vertical columns of supersaturated binary solutions. An analysis and comparison of theoretical results and experimental data related to the solute concentration gradient formation in a gravitational field are presented. It is also demonstrated that the critical radius of solute clusters (radius of nucleation) and induction time are gravity-dependent.

Izmailov, Alexander F.↗

Statistical Perspectives on Stratospheric Transport

Long-lived tropospheric source gases, such as nitrous oxide, enter the stratosphere through the tropical tropopause, are transported throughout the stratosphere by the Brewer-Dobson circulation, and are photochemically destroyed in the upper stratosphere. These chemical constituents, or "tracers" can be used to track mixing and transport by the stratospheric winds. Much of our understanding about the stratospheric circulation is based on large scale gradients and other spatial features in tracer fields constructed from satellite measurements. The point of view presented in this paper is different, but complementary, in that transport is described in terms of tracer probability distribution functions (PDFs). The PDF is computed from the measurements, and is proportional to the area occupied by tracer values in a given range. The flavor of this paper is tutorial, and the ideas are illustrated with several examples of transport-related phenomena, annotated with remarks that summarize the main point or suggest new directions. One example shows how the multimodal shape of the PDF gives information about the different branches of the circulation. Another example shows how the statistics of fluctuations from the most probable tracer value give insight into mixing between different regions of the atmosphere. Also included is an analysis of the time-dependence of the PDF during the onset and decline of the winter circulation, and a study of how "bursts" in the circulation are reflected in transient periods of rapid evolution of the PDF. The dependence of the statistics on location and time are also shown to be important for practical problems related to statistical robustness and satellite sampling. The examples illustrate how physically-based statistical analysis can shed some light on aspects of stratospheric transport that may not be obvious or quantifiable with other types of analyses. An important motivation for the work presented here is the need for synthesis of the large and growing database of observations of the atmosphere and the vast quantities of output generated by atmospheric models.

Sparling, L. C.↗

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗

Exact Solutions to Time-dependent Mdps

We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Boyan, Justin A.↗

Scientific Visualization of Large Scale Unsteady Fluid Flow

In a numerical flow simulation. it is common to generate several thousand time steps of unsteady (time-dependent) flow data. Each time step may require tens to hundreds of megabytes for disk storage, and the total disk requirement for storing the unsteady flow data may be hundreds of gigabytes. Interactive visualization of unsteady flow data of this magnitude is presently impossible with the current hardware technology. This chapter describes the current approaches for unsteady flow visualization. An effective particle tracing technique for unsteady flow is also described. First, the life cycle of a typical numerical flow simulation is outlined. Several unsteady flow data sets from real-world problems are then given. The current approaches for visualizing unsteady flow are then described. There are many existing systems for flow visualization, and some of them are discussed. Streaklines depict time-varying phenomena that are sometimes difficult or impossible to see with other visualization techniques. The algorithms for computing streaklines are described. Several unsteady flow data sets have been visualized using streaklines, and the results are presented. Finally, some current issues in unsteady flow visualization are discussed.

Lane, David A.↗

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Aftosmis, M. J.↗

A New Time-dependent Model for the Martian Radiation Environment

Manned space activities have been until present time limited to the near-Earth environment, most of them to low Earth orbit (LEO) scenarios, with only some of the Apollo missions targeted to the Moon. In current times most human exploration and development of space (HEDS) activities are related to the development of the International Space Station (ISS), and therefore take place in the LEO environment. A natural extension of HEDS activities will be going beyond LEO, and reach asteroids, Mars, Jupiter, Saturn, the Kuiper belt and the outskirts of the Solar System. Such long journeys onboard spacecraft outside the protective umbrella of the geomagnetic field will require higher levels of protection from the radiation environment found in the deep space for both astronauts and equipment. So, it is important to have available a tool for radiation shielding which takes into account the radiation environments found all along the interplanetary space and at the different bodies encountered in the Solar System. Moreover, the radiation protection is one of the two NASA highest concerns and priorities. A tool integrating different radiation environments with shielding computation techniques especially tailored for deep space mission scenario is instrumental in view of this exigency. In view of manned missions targeted to Mars, for which radiation exposure is one of the greatest problems and challenges to be tackled, it is of fundamental importance to have available a tool which allows to know which are the particle flux and spectra at any time at any point of the Martian surface. With this goal in mind, a new model for the radiation environment to be found on the planet Mars due to Galactic Cosmic Rays (GCR) has been developed. Solar modulated primary particles rescaled for Mars conditions are transported within the Martian atmosphere, with temporal properties modeled with variable timescales, down to the surface, with altitude and backscattering patterns taken into account. The tool allows analysis for manned Mars landing missions, as well as planetary science studies, e.g. subsurface water and volatile inventory studies. This Mars environmental model is available through the SIREST website, a project of NASA Langley Research Center.

G De Angelis↗

Relationship Between Vortex Meander and Ambient Turbulence

Efforts are currently underway to increase the capacity of airports by use of closely-spaced parallel runways. If such an objective is to be achieved safely and efficiently during both visual and instrument flight conditions, it will be necessary to develop more precise methods for the prediction of the motion and spread of the hazard posed by the lift-generated vortex-wakes of aircraft, and their uncertainties. The purpose of the present study is to relate the motion induced in vortex filaments by turbulence in the ambient flow field to the measured turbulence in the flow field. The problem came about when observations made in the two largest NASA wind tunnels indicated that extended exposure of vortex wakes to the turbulence in the wind tunnel air stream causes the centers of the vortices to meander about with time at a given downstream station where wake measurements are being made. Although such a behavior was expected, the turbulence level based on the maximum amplitude of meander was much less than the root-mean-squared value measured in the free-stream of the wind tunnel by use of hot-film anemometers. An analysis of the time-dependent motion of segments of vortex filaments as they interact with an eddy, indicates that the inertia of the filaments retards their motion enough in the early part of their travel to account for a large part of the difference in the two determinations of turbulence level. Migration of vortex filaments from one turbulent eddy to another (probably with a different orientation), is believed to account for the remainder of the difference. Methods that may possibly be developed for use in the measurement of the magnitude of the more intense eddies in turbulent flow fields and how they should be adjusted to predict vortex meander are then discussed.

Rossow, Vernon J.↗

New Observations of the Heliospheric Magnetic Field from the Voyager Spacecraft

We review recent observations of variations of the heliospheric magnetic field B(t) made by Voyager 1 and 2 (V1 and V2), and we discuss the boundary conditions needed for models to explain the observations. Usually, observations from a spacecraft close to the Sun, such as ACE, WIND or Ulysses are used as input to a time-dependent model. Generally, the predicted profile B(t) can be compared directly with the observed profile only when either V1 or V2 is approximately radially aligned with a near-Sun spacecraft; this happens rarely and only for a brief time interval. The Bastille Day events illustrate this situation. In the absence of radial alignment of the spacecraft it is possible to predict the development of a global structure (a GMIR) with data from ACE or WIND, if they obtain a representative sample the flows that merge to form a GMIR. When latitudinal gradients are small and when there is statistical homogeneity in the azimuthal direction, it is possible to predict the statistical properties of the large-scale fluctuations of B(t) observed by V1 or V2 during a year or so. We illustrate this situation with observations from the recent solar maximum and the declining phase of the solar cycle. Predictions of detailed observations made by V1 and V2 under general conditions (e.g., when there is a large latitudinal gradient) require boundary conditions as a function of time on a surface, such as a Sun-centered sphere with a radius of 1 AU. These conditions can only be provided by global solar observations. We suggest the feasibility of such an approach, using V2 observations for 2005 and 2006. The prediction of observations in the heliosheath requires the solution of the 3-D boundary problem for the supersonic solar wind and propagation of solar wind through the termination shock into the heliosphere. The properties of B(t) observed in the heliosheath have not yet been predicted.

Burlaga, Leonard F.↗

Progress in Computational Simulation of Earthquakes

GeoFEST(P) is a computer program written for use in the QuakeSim project, which is devoted to development and improvement of means of computational simulation of earthquakes. GeoFEST(P) models interacting earthquake fault systems from the fault-nucleation to the tectonic scale. The development of GeoFEST( P) has involved coupling of two programs: GeoFEST and the Pyramid Adaptive Mesh Refinement Library. GeoFEST is a message-passing-interface-parallel code that utilizes a finite-element technique to simulate evolution of stress, fault slip, and plastic/elastic deformation in realistic materials like those of faulted regions of the crust of the Earth. The products of such simulations are synthetic observable time-dependent surface deformations on time scales from days to decades. Pyramid Adaptive Mesh Refinement Library is a software library that facilitates the generation of computational meshes for solving physical problems. In an application of GeoFEST(P), a computational grid can be dynamically adapted as stress grows on a fault. Simulations on workstations using a few tens of thousands of stress and displacement finite elements can now be expanded to multiple millions of elements with greater than 98-percent scaled efficiency on over many hundreds of parallel processors (see figure).

Donnellan, Andrea↗

Finite-Element Methods for Real-Time Simulation of Surgery

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

Basdogan, Cagatay↗

Electro-Optic Time-to-Space Converter for Optical Detector Jitter Mitigation

A common problem in optical detection is determining the arrival time of a weak optical pulse that may comprise only one to a few photons. Currently, this problem is solved by using a photodetector to convert the optical signal to an electronic signal. The timing of the electrical signal is used to infer the timing of the optical pulse, but error is introduced by random delay between the absorption of the optical pulse and the creation of the electrical one. To eliminate this error, a time-to-space converter separates a sequence of optical pulses and sends them to different photodetectors, depending on their arrival time. The random delay, called jitter, is at least 20 picoseconds for the best detectors capable of detecting the weakest optical pulses, a single photon, and can be as great as 500 picoseconds. This limits the resolution with which the timing of the optical pulse can be measured. The time-to-space converter overcomes this limitation. Generally, the time-to-space converter imparts a time-dependent momentum shift to the incoming optical pulses, followed by an optical system that separates photons of different momenta. As an example, an electro-optic phase modulator can be used to apply longitudinal momentum changes (frequency changes) that vary in time, followed by an optical spectrometer (such as a diffraction grating), which separates photons with different momenta into different paths and directs them to impinge upon an array of photodetectors. The pulse arrival time is then inferred by measuring which photodetector receives the pulse. The use of a time-to-space converter mitigates detector jitter and improves the resolution with which the timing of an optical pulse is determined. Also, the application of the converter enables the demodulation of a pulse position modulated signal (PPM) at higher bandwidths than using previous photodetector technology. This allows the creation of a receiver for a communication system with high bandwidth and high bits/photon efficiency.

Birnbaum, Kevin↗

Measuring Electron Temperature Using a Linear Polarizer Versus a Polarization Camera

Polarized K-coronal brightness (pB) of the solar corona can be measured by taking four successive coronal brightness images through a linear polarizer, by turning it through four successive angles in intervals of 45∘ and using a standard formula to measure pB from the total coronal brightness (TB) that contains both the polarized K- and the unpolarized F-coronal brightness. The question is: will the time-dependent, highly dynamic corona illuminate each pixel with the same brightness during the time it takes to take the four successive images? To mitigate this problem we now have the polarization camera, in which, each super-pixel is made up of four sub-pixels, and built in to these four sub-pixels is a polarization mask that contains four linear polarizers orientated at four angles 45∘ apart. This allows the measurement of pB to be made in a single exposure. Here, the question is: will the variations of the coronal brightness in the four adjacent sub-pixels in a super-pixel be sufficiently negligible to assume that they observe the same part of the corona? This article looks for answers to these two questions by conducting two synthetic experiments to measure the electron temperature in the plane of the sky on a spherically asymmetric model (SAM) corona by first using a linear polarizer, and then replacing it with a polarization camera and use statistical analyses to determine how well the measured temperature matched the true temperature for the two cases.

Reginald, Nelson↗

Utilization of Machine Learning Techniques for Managing the Tracking and Data Relay Satellite Constellation

National Aeronautics and Space Administration’s (NASA) Goddard Space Flight Center (GSFC) operates a constellation of ten geosynchronous Tracking and Data Relay Satellites (TDRS). The TDRS constellation consists of multiple geosynchronous communication relay satellites located around the equator so they can provide continual coverage of any mission in low earth orbit. The TDRS are located primarily in three oceanic regions around the earth. NASA’s White Sands Complex provides the ground communication support for TDRS located over the Atlantic and Pacific Oceans. Another TDRS ground station in Guam supports the TDRS over the Indian Ocean. With these satellites the TDRS network can provide continuous coverage of satellites in low-earth orbit. The NASA Space Network (SN) project office at GSFC manages the constellation of spacecraft. Major customers of the TDRS constellation include, but are not limited to, the International Space Station and the Hubble Space Telescope. The TDRS constellation has three generations of satellites and has been active for over 30 years providing reliable communication links between customer satellites and corresponding ground stations. However, one of the major concerns for TDRS, and in any space mission, is to ensure the health and safety of the spacecraft. Generally, engineers use telemetry data to monitor and analyze the performance and state of health of the spacecraft. Telemetry data contains hundreds of parameters that monitor each important component in the spacecraft, which can be utilized to recognize and characterize the behavior of the spacecraft. Each parameter contains considerable information to represent time-dependent properties of each spacecraft subsystem and component. During the entire life of a TDRS spacecraft, thousands of gigabytes of telemetry data are transmitted in real-time from the spacecraft to the ground station at the White Sands Complex in Las Cruces, New Mexico, and recorded as historical data sets for engineers to process and analyze the events that occurred on-orbit. These parameters contain the function of multiple spacecraft subsystems, such as the attitude control system (ACS), Thermal, Electrical Power Subsystem (EPS), etc. . The first and second generations have exceeded their required lifetime and NASA is keen to manage these spacecrafts carefully in order to maximize the remaining life using the spacecraft telemetry. The challenge is to know when the risk of losing a spacecraft in geosynchronous orbit exceeds the benefit of continued operations for customer support. In the TDRS fleet, the EPS is the most critical subsystem related to spacecraft operations. Failure of the EPS would strand a spacecraft in geosynchronous orbit. Since EPS provides power to the spacecraft, component failures ultimately lead to the inability to support the spacecraft loads and the communications payload. For instance, TDRS-8 has several anomalies in EPS including the Bus Voltage Limiter (BVL) shunt current, solar array loss of circuits, and failed battery cells. Any of these anomalies can cause critical issues to the spacecraft. Therefore, developing a system to analyze and perform early detection of a potential anomaly is an important issue in telemetry data analysis. In recent years, Telemetry Mining (TM) has been proposed to process telemetry data by using Data Mining (DM) techniques such as classification, clustering, regression and anomaly detection. Anomaly detection, also known as outlier detection, has been widely used in many data mining areas such as remote sensing, medical data processing and digital image processing. The goal of anomaly detection is to detect abnormal data, which contains a relatively low probability of occurrence among the entire data set. Early detection of anomalies is one of the most significant issues in managing the spacecraft configuration. If anomalies can be detected early enough, then the redundant resources can be used to extend the life of the operational spacecraft. We present an unsupervised anomaly detection method to process the EPS data extracted from TDRS-8. This is different from traditional analytical methods, which use telemetry data to illustrate behavior and physical meaning of each spacecraft component. TM connects multiple parameters as a vector and then conducts data analysis on this high dimension telemetry vector. This method is looking at the properties of a high dimensional vector that is able to consider the relationship between different parameters in the anomaly detection problem. This kind of method performs much better than the traditional limit checking method. In addition, we propose a new approach of real-time anomaly detection to process telemetry data in real-time, which can then be applied to spacecraft monitoring with high reliability, low cost and high accuracy.

Machine Learning (ML)↗

Evaluating the De Hoffmann-Teller Cross-Shock 2 Potential at Real Collisionless Shocks

Shock waves are common in the heliosphere and beyond. The collisionless nature of most astrophysical plasmas allows for the energy processed by shocks to be partitioned amongst particle sub-populations and electromagnetic fields via physical mechanisms that are not well understood. The electrostatic potential across such shocks is frame dependent. In a frame where the incident bulk velocity is parallel to the magnetic field, the deHoffmann-Teller frame, the potential is linked directly to the ambipolar electric field established by the electron pressure gradient. Thus measuring and understanding this potential solves the electron partition problem, and gives insight into other competing shock processes. Integrating measured electric fields in space is problematic since the measurements can have offsets that change with plasma conditions. The offsets, once integrated, can be as large or larger than the shock potential. Here we exploit the high-quality field and plasma measurements from NASA’s Magnetospheric Multiscale mission to attempt this calculation. We investigate recent adaptations of the deHoffmann-Teller frame transformation to include time variability, and conclude that in practice these face difficulties inherent in the 3D time-dependent nature of real shocks by comparison to 1D simulations. Potential estimates based on electron fluid and kinetic analyses provide the most robust measures of the deHoffmann-Teller potential, but with some care direct integration of the electric fields can be made to agree. These results suggest that it will be difficult to independently assess the role of other processes, such as scattering by shock turbulence, in accounting for the electron heating.

Steven J Schwartz↗

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions to the finite element problem, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization↗