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High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy

Computational study of duct and pipe flows using the method of pseudocompressibility

A viscous, three-dimensional, incompressible, Navier-Stokes Computational Fluid Dynamics code employing pseudocompressibility is used for the prediction of laminar primary and secondary flows in two 90-degree bends of constant cross section. Under study are a square cross section duct bend with 2.3 radius ratio and a round cross section pipe bend with 2.8 radius ratio. Sensitivity of predicted primary and secondary flow to inlet boundary conditions, grid resolution, and code convergence is investigated. Contour and velocity versus spanwise coordinate plots comparing prediction to experimental data flow components are shown at several streamwise stations before, within, and after the duct and pipe bends. Discussion includes secondary flow physics, computational method, computational requirements, grid dependence, and convergence rates.

Williams, Robert W.

Hybrid Modeling Study on Grain Evolution in the Metal Welding Process and Its Potential Lunar Application

Metal is most commonly used structural material in a wide range of spacecraft, and welding is the principal method for joining metal components into functional systems. However, conducting welding experiments under extreme environments—such as microgravity or vacuum conditions in space—is prohibitively expensive and experimentally challenging. To overcome these limitations, multi-physics computational welding models provide a cost-effective and versatile alternative. In this work, the authors have developed a coupled thermal (fluid) microstructure simulation framework to model metal welding under varying gravity conditions. The framework integrates a mixed-mode heat transfer formulation (conduction, convection, and radiation) with molten pool fluid dynamics, enabling accurate prediction of temperature fields and weld-pool geometry. A grain growth model is further incorporated to capture the spatial and temporal evolution of microstructure, including grain size distribution and morphological transitions during solidification. This approach provides detailed insight into molten pool evolution and grain-level microstructure development throughout the welding process. By explicitly parameterizing environmental conditions, the model supports extrapolation to off-Earth manufacturing scenarios such as welding on the lunar surface. Tantalum—chosen in this study due to its high melting point, oxidation resistance, and mechanical stability at elevated temperatures—serves as the material system for model demonstration. Beyond Tantalum, the integrated multi-physics framework offers broad applicability for predictive welding simulations of various structural and refractory metals or alloys used in extreme terrestrial or extraterrestrial environments.

kinetic Monte Carlo (SPPARKS)

Applications of numerical codes to space plasma problems

Solar wind, earth's bowshock, and magnetospheric convection and substorms were investigated. Topics discussed include computational physics, multifluid codes, ionospheric irregularities, and modeling laser plasmas.

Northrop, T. G.

Time-dependent computational studies of flames in microgravity

The research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of the NASA Microgravity Science and Applications Program is described. The primary focus was on investigating fundamental questions concerning the propagation and extinction of premixed flames in Earth gravity and in microgravity environments. The approach was to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. A combination of one-dimensional and two-dimensional simulations was used to investigate the effects of curvature and dilution on ignition and propagation of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the mechanism leading to cellular instability, and to study the effects of gravity on the transition to cellular structure. A flame in a microgravity environment can be extinguished without external losses, and the mechanism leading to cellular structure is not preferential diffusion but a thermo-diffusive instability. The simulations have also lead to a better understanding of the interactions between buoyancy forces and the processes leading to thermo-diffusive instability.

Oran, Elaine S.

Laboratory studies, analysis, and interpretation of the spectra of hydrocarbons present in planetary atmospheres including cyanoacetylene, acetylene, propane, and ethane

Combining broadband Fourier transform spectrometers (FTS) from the McMath facility at NSO and from NRC in Ottawa and narrow band TDL data from the laboratories with computational physics techniques has produced a broad range of results for the study of planetary atmospheres. Motivation for the effort flows from the Voyager/IRIS observations and the needs of Voyager analysis for laboratory results. In addition, anticipation of the Cassini mission adds incentive to pursue studies of observed and potentially observable constituents of planetary atmospheres. Current studies include cyanoacetylene, acetylene, propane, and ethane. Particular attention is devoted to cyanoacetylen (H3CN) which is observed in the atmosphere of Titan. The results of a high resolution infrared laboratory study of the line positions of the 663, 449, and 22.5/cm fundamental bands are presented. Line position, reproducible to better than 5 MHz for the first two bands, are available for infrared astrophysical searches. Intensity and broadening studies are in progress. Acetylene is a nearly ubiquitous atmospheric constituent of the outer planets and Titan due to the nature of methane photochemistry. Results of ambient temperature absolute intensity measurements are presented for the fundamental and two two-quantum hotband in the 730/cm region. Low temperature hotband intensity and linewidth measurements are planned.

Blass, William E.

Hypersonic forebody lift-induced drag

The dominance of body-like shapes for hypersonic vehicles places emphasis on better understanding of pertinenet body flow physics. Computational methods are implemented to enhance the knowledge of drag components generated by the production of lift forces at hypersonic speeds. Three forebody shapes are examined to identify the effects related to body shape parameters. A Navier-Stokes code and classical Newtonian theory code provide predictions of the polar shapes upon which conclusions are drawn. In particular, it is noted that hypersonic body polar shapes are somewhat irregular; the result of incidence-induced form drag. Test data which supports this finding is identified. The means for reducing hypersonic body lift-induced drag are also identified, along with applied computational schemes that can reduce the cost of a configuration design program.

Boppe, C. W.

Hypercubes for critical spacecraft command verification

Interplanetary spacecraft are controlled with sets of onboard commands called 'sequences' that control the spacecraft for hours, days, or weeks depending upon the craft and its current activity phase. The sequence-checking problem, with some examples from practical experience, and the technical challenges of implementing sequence checking on a parallel computer are presented. Hypercube applications including computational-physics problems, 'optimistic' and 'conservative' categories are discussed. Finally, future development and prototype ways of balancing the checking network across the hypercube nodes, handling time dependencies among the checks, and minimizing communication are described.

Horvath, Joan C.

Validation and applications of the POLAR code

The Potentials of Large Objects in the Auroral Region (POLAR) code was written to model the charging of large spacecraft by auroral electrons in low polar orbit. It has also proven to be a powerful tool for analysis of active and voltage-plasma interactions. POLAR combines 3-D object definition, direct solution to Poisson's equation, space charge transport, and surface charge computation. Physical effects treated by POLAR include the plasma wake and ram, the geomagnetic field, ionization, sheath and barrier formation, and photo and secondary electron generation and transport. Polar development is complete and it is now available to the aerospace community. The methodology of POLAR is reviewed but concentration is on the applications of POLAR to physical problems and observations with the intent of demonstrating both the code's capabilities, and its limitations. These applications include the Space Shuttle, the Defense Meteorological Satellite Program (DMSP) satellites, sounding rockets, plasma chamber experiments, and things not yet flown.

Cooke, David L.

Time-dependent Computational Studies of Premixed Flames in Microgravity

This report describes the research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of NASA Microgravity Science and Applications Program. The primary focus of this research is on investigating fundamental questions concerning the propagation and extinction of premixed flames in earth gravity and in microgravity environments. Our approach is to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. Recently more advanced wall boundary conditions such as isothermal and no-slip have been added to the model. This enables the simulation of flames propagating in more practical systems than before. We have used the numerical simulations to investigate the effects of heat losses and buoyancy forces on the structure and stability of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the interaction between the various processes leading to flame instabilities and extinguishment, and to study the dynamics of cell formation and splitting. Our studies have been able to bring out the differences between upward- and downward-propagating flames and predict the zero-gravity behavior of these flames. The simulations have also highlighted the dominant role of wall heat losses in the case of downward-propagating flames. The simulations have been able to qualitatively predict the formation of multiple cells and the cessation of cell-splitting. Our studies have also shown that some flames in a microgravity environment can be extinguished due to a chemical instability and without any external losses. However, further simulations are needed to more completely understand upward-propagating and zero-gravity flames as well as to understand the potential effect of radiative heat losses.

Kailasanath, K.

Particle-mesh techniques

This is an introduction to numerical Particle-Mesh techniques, which are commonly used to model plasmas, gravitational N-body systems, and both compressible and incompressible fluids. The theory behind this approach is presented, and its practical implementation, both for serial and parallel machines, is discussed. This document is based on a four-hour lecture course presented by the author at the NASA Summer School for High Performance Computational Physics, held at Goddard Space Flight Center.

Macneice, Peter

Department of Physics' Involvement of the Impact Testing Project of the High Speed Civil Transport Program (HSCT)

The project involved the impact testing of a kevlar-like woven polymer material, PBO. The purpose was to determine whether this material showed any promise as a lightweight replacement material for jet engine fan containment. The currently used metal fan containment designs carry a high drag penalty due to their weight. Projectiles were fired at samples of PBO by means of a 0.5 inch diameter Helium powered gun. The Initial plan was to encase the samples inside a purpose-built steel "hot box" for heating and ricochet containment. The research associate's responsibility was to develop the data acquisition programs and techniques necessary to determine accurately the impacting projectile's velocity. Beyond this, the Research Associate's duties include any physical computations, experimental design, and data analysis necessary.

VonMeerwall, Ernst D.

Gravitational-Wave Astronomy

Einstein's General Theory of Relativity is our best classical description of gravity, and informs modern astronomy and astrophysics at all scales: stellar, galactic, and cosmological. Among its surprising predictions is the existence of gravitational waves -- ripples in space-time that carry energy and momentum away from strongly interacting gravitating sources. In my talk, I will give an overview of the properties of this radiation, recent breakthroughs in computational physics allowing us to calculate the waveforms from galactic mergers, and the prospect of direct observation with interferometric detectors such as LIGO and LISA.

Kelly, Bernard J.

Solar Radiation Transport in the Cloudy Atmosphere: A 3D Perspective on Observations and Climate Impacts

The interplay of sunlight with clouds is a ubiquitous and often pleasant visual experience, but it conjures up major challenges for weather, climate, environmental science and beyond. Those engaged in the characterization of clouds (and the clear air nearby) by remote sensing methods are even more confronted. The problem comes, on the one hand, from the spatial complexity of real clouds and, on the other hand, from the dominance of multiple scattering in the radiation transport. The former ingredient contrasts sharply with the still popular representation of clouds as homogeneous plane-parallel slabs for the purposes of radiative transfer computations. In typical cloud scenes the opposite asymptotic transport regimes of diffusion and ballistic propagation coexist. We survey the three-dimensional (3D) atmospheric radiative transfer literature over the past 50 years and identify three concurrent and intertwining thrusts: first, how to assess the damage (bias) caused by 3D effects in the operational 1D radiative transfer models? Second, how to mitigate this damage? Finally, can we exploit 3D radiative transfer phenomena to innovate observation methods and technologies? We quickly realize that the smallest scale resolved computationally or observationally may be artificial but is nonetheless a key quantity that separates the 3D radiative transfer solutions into two broad and complementary classes: stochastic and deterministic. Both approaches draw on classic and contemporary statistical, mathematical and computational physics.

Davis, Anthony B.

Developments in Atmosphere Revitalization Modeling and Simulation

"NASA's Advanced Exploration Systems (AES) program is pioneering new approaches for rapidly developing prototype systems, demonstrating key capabilities, and validating operational concepts for future human missions beyond Earth orbit" (NASA 2012). These forays beyond the confines of earth's gravity will place unprecedented demands on launch systems. They must not only blast out of earth's gravity well as during the Apollo moon missions, but also launch the supplies needed to sustain a crew over longer periods for exploration missions beyond earth's moon. Thus all spacecraft systems, including those for the separation of metabolic carbon dioxide and water from a crewed vehicle, must be minimized with respect to mass, power, and volume. Emphasis is also placed on system robustness both to minimize replacement parts and ensure crew safety when a quick return to earth is not possible. Current efforts are focused on improving the current state-of-the-art systems utilizing fixed beds of sorbent pellets by evaluating structured sorbents, seeking more robust pelletized sorbents, and examining alternate bed configurations to improve system efficiency and reliability. These development efforts combine testing of sub-scale systems and multi-physics computer simulations to evaluate candidate approaches, select the best performing options, and optimize the configuration of the selected approach, which is then implemented in a full-scale integrated atmosphere revitalization test. This paper describes the development of atmosphere revitalization models and simulations. A companion paper discusses the hardware design and sorbent screening and characterization effort in support of the Atmosphere Revitalization Recovery and Environmental Monitoring (ARREM) project within the AES program.

Knox, James C.

Development of Carbon Dioxide Removal Systems for Advanced Exploration Systems

"NASA's Advanced Exploration Systems (AES) program is pioneering new approaches for rapidly developing prototype systems, demonstrating key capabilities, and validating operational concepts for future human missions beyond Earth orbit" (NASA 2012). These forays beyond the confines of earth's gravity will place unprecedented demands on launch systems. They must not only blast out of earth's gravity well as during the Apollo moon missions, but also launch the supplies needed to sustain a crew over longer periods for exploration missions beyond earth's moon. Thus all spacecraft systems, including those for the separation of metabolic carbon dioxide and water from a crewed vehicle, must be minimized with respect to mass, power, and volume. Emphasis is also placed on system robustness both to minimize replacement parts and ensure crew safety when a quick return to earth is not possible. Current efforts are focused on improving the current state-of-the-art systems utilizing fixed beds of sorbent pellets by seeking more robust pelletized sorbents, evaluating structured sorbents, and examining alternate bed configurations to improve system efficiency and reliability. These development efforts combine testing of sub-scale systems and multi-physics computer simulations to evaluate candidate approaches, select the best performing options, and optimize the configuration of the selected approach, which is then implemented in a full-scale integrated atmosphere revitalization test. This paper describes the carbon dioxide (CO2) removal hardware design and sorbent screening and characterization effort in support of the Atmosphere Resource Recovery and Environmental Monitoring (ARREM) project within the AES program. A companion paper discusses development of atmosphere revitalization models and simulations for this project.

Knox, James C.

Additional Developments in Atmosphere Revitalization Modeling and Simulation

NASA's Advanced Exploration Systems (AES) program is developing prototype systems, demonstrating key capabilities, and validating operational concepts for future human missions beyond Earth orbit. These forays beyond the confines of earth's gravity will place unprecedented demands on launch systems. They must launch the supplies needed to sustain a crew over longer periods for exploration missions beyond earth's moon. Thus all spacecraft systems, including those for the separation of metabolic carbon dioxide and water from a crewed vehicle, must be minimized with respect to mass, power, and volume. Emphasis is also placed on system robustness both to minimize replacement parts and ensure crew safety when a quick return to earth is not possible. Current efforts are focused on improving the current state-of-the-art systems utilizing fixed beds of sorbent pellets by evaluating structured sorbents, seeking more robust pelletized sorbents, and examining alternate bed configurations to improve system efficiency and reliability. These development efforts combine testing of sub-scale systems and multi-physics computer simulations to evaluate candidate approaches, select the best performing options, and optimize the configuration of the selected approach. This paper describes the continuing development of atmosphere revitalization models and simulations in support of the Atmosphere Revitalization Recovery and Environmental Monitoring (ARREM)

Coker, Robert F.

Development of a Prototype Algal Reactor for Removing CO2 from Cabin Air

Controlling carbon dioxide in spacecraft cabin air may be accomplished using algal photobioreactors (PBRs). The purpose of this project was to evaluate the use of a commercial microcontroller, the Arduino Mega 2560, for measuring key phot~ioreactor variables: dissolved oxygen, pH, temperature, light, and carbon dioxide. The Arduino platform is an opensource physical computing platform composed of a compact microcontroller board and a C++/C computer language (Arduino 1.0.5). The functionality of the Arduino platform can be expanded by the use of numerous add-ons or 'shields'. The Arduino Mega 2560 was equipped with the following shields: datalogger, BNC shield for reading pH sensor, a Mega Moto shield for controlling CO2 addition, as well as multiple sensors. The dissolved oxygen (DO) probe was calibrated using a nitrogen bubbling technique and the pH probe was calibrated via an Omega pH simulator. The PBR was constructed using a 2 L beaker, a 66 L box for addition of CO2, a micro porous membrane, a diaphragm pump, four 25 watt light bulbs, a MasterFiex speed controller, and a fan. The algae (wild type Synechocystis PCC6803) was grown in an aerated flask until the algae was dense enough to used in the main reactor. After the algae was grown, it was transferred to the 2 L beaker where CO2 consumption and O2 production was measured using the microcontroller sensor suite. The data was recorded via the datalogger and transferred to a computer for analysis.

Patel, Vrajen