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At least 1,189 records · Page 66

Experimental Investigation of Crossing Shock Wave-Turbulent Boundary Layer-Bleed Interaction

Results of an experimental investigation of a symmetric crossing shock wave/turbulent boundary layer/bleed interaction are presented for a freestream unit Reynolds number of 1.68 x 10(exp 7)/m, a Mach number of 2.81, and deflection angles of 8 degrees. The data obtained in this study are bleed mass flow rate using a trace gas technique, qualitative information in the form of oil flow visualization, flow field Pitot pressures, and static pressure measurements using pressure sensitive paint. The main objective of this test is two-fold. First, this study is conducted to explore boundary layer control through mass flow removal near a large region of separated flow caused by the interaction of a double fin-induced shock wave and an incoming turbulent boundary layer. Also, a comprehensive data set is needed for computational fluid dynamics code validation.

Kim, Hyun↗

Experimental Investigation of the Near Wall Flow Structure of a Low Reynolds Number 3-D Turbulent Boundary Layer

Laser Doppler velocimetry (LDV) measurements and hydrogen bubble flow visualization techniques were used to examine the near-wall flow structure of 2D and 3D turbulent boundary layers (TBLs) over a range of low Reynolds numbers. The goals of this research were (1) an increased understanding of the flow physics in the near wall region of turbulent boundary layers,(2) to observe and quantify differences between 2D and 3D TBL flow structures, and (3) to document Reynolds number effects for 3D TBLs. The LDV data have provided results detailing the turbulence structure of the 2D and 3D TBLs. These results include mean Reynolds stress distributions, flow skewing results, and U and V spectra. Effects of Reynolds number for the 3D flow were also examined. Comparison to results with the same 3D flow geometry but at a significantly higher Reynolds number provided unique insight into the structure of 3D TBLs. While the 3D mean and fluctuating velocities were found to be highly dependent on Reynolds number, a previously defined shear stress parameter was discovered to be invariant with Reynolds number. The hydrogen bubble technique was used as a flow visualization tool to examine the near-wall flow structure of 2D and 3D TBLs. Both the quantitative and qualitative results displayed larger turbulent fluctuations with more highly concentrated vorticity regions for the 2D flow.

FLOW VISUALIZATION↗

New Third-Order Moments for the CBL

Turbulent convection is an inherently non-local phenomenon and a primary condition for a successful treatment of the CBL (convective boundary layer) is a reliable model of non-locality. In the dynamic equations governing the convective flux, the turbulent kinetic energy, etc., non-locality is represented by the third-order moments, TOMs. Since the simplest form, the so-called down gradient approximation (DGA), severely underestimates the TOMs (up to an order of magnitude), a more physical model is needed. In 1994, an analytical model was presented which was derived directly from the dynamical equations for the TOMs. It considerably improved the DGA but was a bit cumbersome to use and, more importantly, it was based on the quasi-normal (QN) approximation for the fourth-order moments. Here, we present a new analytic expression for the TOMs which is structurally simpler than the 1994 expression and which avoids the QN approximation. The resulting fit to the LES data is superior to that of the 1994 model.

Canuto, V. M.↗

Modelling the Centers of Galaxies

The key to studying central regions by means of nobody numerical experiments is to concentrate on the central few parsecs of a galaxy, replacing the remainder of the galaxy by a suitable boundary condition, rather after the manner in which stellar interiors can be studied without a detailed stellar atmosphere by replacing the atmosphere with a boundary condition. Replacements must be carefully designed because the long range gravitational force means that the core region is sensitive to mass outside that region and because particles can exchange between the outer galaxy and the core region. We use periodic boundary conditions, coupled with an iterative procedure to generate initial particle loads in isothermal equilibrium. Angular momentum conservation is ensured for problems including systematic rotation by a circular reflecting boundary and by integrating in a frame that rotates with the mean flow. Mass beyond the boundary contributes to the gravitational potential, but does not participate in the dynamics. A symplectic integration scheme has been developed for rotating coordinate systems. This combination works well, leading to robust configurations. Some preliminary results with this combination show that: (1) Rotating systems are extremely sensitive to non-axisymmetric external potentials, and (2) that a second core, orbiting near the main core (like the M31 second core system), shows extremely rapid orbital decay. The experimental setups will be discussed, along with preliminary results.

Smith, B. F.↗

Assessment of NASA GISS CMIP5 and Post-CMIP5 Simulated Clouds and TOA Radiation Budgets Using Satellite Observations. Part I: Cloud Fraction and Properties

Although many improvements have been made in phase 5 of the Coupled Model Intercomparison Project (CMIP5), clouds remain a significant source of uncertainty in general circulation models (GCMs) because their structural and optical properties are strongly dependent upon interactions between aerosol/cloud microphysics and dynamics that are unresolved in such models. Recent changes to the planetary boundary layer (PBL) turbulence and moist convection parameterizations in the NASA GISS Model E2 atmospheric GCM(post-CMIP5, hereafter P5) have improved cloud simulations significantly compared to its CMIP5 (hereafter C5) predecessor. A study has been performed to evaluate these changes between the P5 and C5 versions of the GCM, both of which used prescribed sea surface temperatures. P5 and C5 simulated cloud fraction (CF), liquid water path (LWP), ice water path (IWP), cloud water path (CWP), precipitable water vapor (PWV), and relative humidity (RH) have been compared to multiple satellite observations including the Clouds and the Earth's Radiant Energy System-Moderate Resolution Imaging Spectroradiometer (CERES-MODIS, hereafter CM), CloudSat- Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO; hereafter CC), Atmospheric Infrared Sounder (AIRS), and Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). Although some improvements are observed in the P5 simulation on a global scale, large improvements have been found over the southern midlatitudes (SMLs), where correlations increased and both bias and root-mean-square error (RMSE) significantly decreased, in relation to the previous C5 simulation, when compared to observations. Changes to the PBL scheme have resulted in improved total column CFs, particularly over the SMLs where marine boundary layer (MBL) CFs have increased by nearly 20% relative to the previous C5 simulation. Globally, the P5 simulated CWPs are 25 gm22 lower than the previous C5 results. The P5 version of the GCM simulates PWV and RH higher than its C5 counterpart and agrees well with the AMSR-E and AIRS observations. The moister atmospheric conditions simulated by P5 are consistent with the CF comparison and provide a strong support for the increase in MBL clouds over the SMLs. Over the tropics, the P5 version of the GCM simulated total column CFs and CWPs are slightly lower than the previous C5 results, primarily as a result of the shallower tropical boundary layer in P5 relative to C5 in regions outside the marine stratocumulus decks.

General circulation models↗

Rough-Wall Turbulent Heat Transfer Experiments in Hypersonic Free Flight

Experiments are being conducted in the NASA Ames Hypervelocity Free Flight Aerodynamic Facility to quantify the effects on turbulent convective heat transfer of surface roughness representative of a new class of 3D woven thermal protection system mRough-wall turbulent heat transfer measurements were obtained on ballistic-range models in hypersonic flight in the NASA Ames Hypervelocity Free Flight Aerodynamic Facility. Each model had three different surface textures on segments of the conic frustum: smooth wall, sand roughness, and a pattern roughness, thus providing smooth-wall and sand-roughness reference data for each test. The pattern roughness was representative of a woven thermal protection system material developed by NASA's Heatshield for Extreme Entry Environment Technology project. The tests were conducted at launch speeds of 3.2 km/s in air at 0.15 atm. Roughness Reynolds numbers, k+, ranged for 12 to 70 for the sand roughness, and as high as 200 for the pattern roughness. Boundary-layer parameters required for calculating k+ were evaluated using computational fluid dynamics simulations. The effects of pattern roughness are generally characterized by an equivalent sand roughness determined with a correlation developed from experimental data obtained on specifically-designed roughness patterns that do not necessarily resemble real TPS materials. Two sand roughness correlations were examined: Dirling and van Rij, et al. Both gave good agreement with the measured heat-flux augmentation for the two larger pattern roughness heights tested, but not for the smallest height tested. It has yet to be determined whether this difference is due to limitations in the experimental approach, or due to limits in the correlations used. Future experiments are planned that will include roughness patterns more like those used in developing the equivalent sand roughness correlations.aterials being developed by NASA's Heatshield for Extreme Entry Environment Technology (HEEET) project. Data were simultaneously obtained on sand-grain roughened surfaces and smooth surfaces, which can be compared with previously obtained data. Results are presented in this extended abstract for one roughness pattern. The full paper will include results from three roughness patterns representing virgin HEEET, nominal turbulent ablated HEEET, and twice the roughness of nominal turbulent ablated HEEET. Results will be used to compare with commonly used equivalent sand grain roughness correlations.

pattern roughness↗

Sketch-to-Solution: A Case Study in RCS Aerodynamic Interaction

Thanks to recent advances in the fields of anisotropic grid adaptation, error estimation, and geometry modeling, a sketch-to-solution work flow is now possible for viscous computational fluid dynamic (CFD) simulations. With this workflow, a CFD application engineer provides geometry, boundary conditions, and flow parameters; and the sketch-to-solution process yields a CFD simulation through automatic, error-based, grid adaptation. To explore the benefits of this nascent capability, a conventional manual grid generation work flow is compared to this new automatic grid generation work flow for a given engineering question: What are the aerodynamic interactions caused by the reaction control system (RCS) on an entry vehicle? This case study indicates that while the automatic grid generation sketch-to- solution process is not yet mature, it is preferred over a manual grid generation work flow because it greatly reduces manual labor, eliminates many opportunities for human error, and provides grid sensitivity information.

Bill Kleb↗

Assessing the Effects of Various Surface Textures and Features on Turbulent Heat Transfer in Hypersonic Flight

Experiments were conducted in the NASA Ames Hypervelocity Free Flight Aerodynamic Facility (ballistic range) to quantify the effects on turbulent convective heat transfer of distributed surface roughness, and of isolated features, representative of thermal protection systems on atmospheric entry vehicles. The surface textures and features were applied on the conic frusta of 45o sphere-cone models having a nose-to-base radius ratio of 0.5, similar to the forebody geometry of the Galileo and Pioneer-Venus entry probes. Test conditions were selected to provide turbulent roughness Reynolds numbers, k+, in the ranges expected for outer planet entry missions. Turbulent flow on the conic frustum was achieved by tripping the flow on the sphere-segment nose cap with distributed surface roughness, created by sand-blasting the nose cap. Surface textures included distributed, acreage, roughness, as well as cavity and groove discrete features. The majority of the data to be presented are results for distributed roughness, which includes both random, sand-grain-like roughness, and regular pattern roughness. The pattern roughness was designed to represent the roughness on woven thermal protection system materials, such as NASA’s 3-D Medium Density Carbon Phenolic (3MDCP), also known as HEEET, developed by the Heatshield for Extreme Entry Environments Technology project. The pattern roughness tested is a 3-D wavy surface, and includes three different roughness element height-to-spacing ratios representative of two configurations of 3MDCP, and spanning ratios measured both before, and after, ablation in an arc jet test facility. The patterns tested in the ballistic range were laser-etched on metal models, and represented an idealized version of the real-world materials in which each roughness element was nearly identical. Additional tests were performed wherein the laser-etched patterns were degraded by sand-blasting with various sized grit media, to produce regular patterns with superimposed irregular roughness, more representative of flight materials. Results of each will be compared. The discrete features tested included cylindrical cavities and rectangular grooves of various width-to-depth ratios. Cavities represent either heatshield damage, such as from micro-meteoroid and orbital debris (MMOD) damage, or from designed penetrations, such as on the Genesis sample return capsule. The grooves were scaled representations of seams between segments of HEEET material in a notional tiled thermal protection system. The tests examined the effects on turbulent heating downstream of the isolated features. The tests were conducted at speeds between 3 km/s and 4 km/s in air between 0.15 atm and 0.25 atm (Mach numbers between 9 and 12). Roughness Reynolds numbers, k+, ranged from 12 to 70 for the sand roughness, and as high as 200 for the pattern roughness. Boundary-layer parameters required for calculating k+ were evaluated using computational fluid dynamics simulations using the DPLR (Data Parallel Line Relaxation) code. Each model included both rough- and smooth-wall segments, and heat transfer augmentation factors were determined as the ratio of the rough-wall to smooth-wall heat flux measured on each test.

hypersonic↗

Dynamical characteristics of cirrus clouds from aircraft and radar measurements

Cirrus clouds play an important role in climate and in the development of other types of clouds. Although there are many studies of clouds within the boundary layer, cirrus clouds have been neglected up until the last decade. New tools and in-situ measurements of various physical and dynamical parameters permit us to now study cirrus clouds in much greater detail. Physical and dynamical structures of cirrus clouds were studied in detail by Heymsfield using aircraft measurements. He emphasized the importance of interactions among physical and dynamical processes. Cirrus clouds often exhibit complex physical and dynamical structure. Upper tropospheric flows contain not only coherent structures, but also chaotic movements. The coherent structures (organized movements) transfer significant amounts of heat and momentum while their form, size, and intensity depend strongly on environmental instability. Various dynamical structures including cells, waves, and turbulence are studied in order to understand cirrus cloud formation and development.

Gultepe, I.↗

Cross-equatorial and boundary layer exchange: A FGGE review

The Global Weather Experiment (FGGE) provided unique data on the interesting phenomenon of cross-equatorial flow. Such motion is a key element of the seasonal cycle of the tropics, especially in monsoonal regions. The IIb obserations, IIIb assimilations, and implied dynamics of the flows are reviewed. Additional emphasis is given to the low level branches concentrated in the planetary boundary layer, including air sea interaction and vertical turbulence processes. The results of a recent MONEX Boundary Layer Workshop are summarized.

Young, J. A.↗

Propulsion Aeroelastic Analysis Developed for Flutter and Forced Response

The NASA Glenn Research Center at Lewis Field develops new technologies to increase the fuel efficiency of aircraft engines, improve the safety of engine operation, reduce emissions, and reduce engine noise. With the development of new designs for fans, compressors, and turbines to achieve these goals, the basic aeroelastic requirements are that there should be no flutter (self-excited vibrations) or high resonant blade stresses (due to forced response) in the operating regime. Therefore, an accurate prediction and analysis capability is required to verify the aeroelastic soundness of the designs. Such a three-dimensional viscous propulsion aeroelastic analysis capability has been developed at Glenn with support from the Advanced Subsonic Technology (AST) program. This newly developed aeroelastic analysis capability is based on TURBO, a threedimensional unsteady aerodynamic Reynolds-averaged Navier-Stokes turbomachinery code developed previously under a grant from Glenn. TURBO can model the viscous flow effects that play an important role in certain aeroelastic problems such as flutter with flow separation, flutter at high loading conditions near the stall line (stall flutter), flutter in the presence of shock and boundary-layer interaction, and forced response due to wakes and shock impingement. In aeroelastic analysis, the structural dynamics representation of the blades is based on normal modes. A finite-element analysis code is used to calculate these in-vacuum vibration modes and the associated natural frequencies. In an aeroelastic analysis using the TURBO code, flutter and forced response are modeled as being uncoupled. To calculate if a blade row will flutter, one prescribes the motion of the blade to be a harmonic vibration in a specified in-vacuum normal mode. An aeroelastic analysis preprocessor is used to generate the displacement field required for the analysis. The work done by aerodynamic forces on the vibrating blade during a cycle of vibration is calculated. If this work is positive, the blade is dynamically unstable, since it will extract energy from the flow, leading to an increase in the blade s oscillation amplitude. The forced-response excitations on a blade row are calculated by modeling the flow through two adjacent blade rows using the TURBO code. The blades are assumed to be rigid. As an option, a single blade row can be modeled with the upstream blade row influence represented by a time-varying disturbance (gust) at the inlet boundary. The unsteady forces on a blade row from such analyses are used in a structural analysis along with the blade structural dynamics characteristics and aerodynamic damping associated with blade vibration to calculate the resulting dynamic stresses on the blade.

Bakhle, Milind A.↗

Petermann Glacier on the Brink: Progress, Challenges and Insights

Petermann Glacier, the largest marine-terminating glacier in northern Greenland based on catchment area and ice discharge, plays a key role in regulating ice discharge from the Greenland Ice Sheet into the Arctic Ocean. With an upstream catchment connected to the ice sheet interior via a deep subglacial canyon, its future stability has major implications for sea level rise. In this review, we synthesize recent advances in understanding Petermann’s dynamics across three critical interfaces: the ice–ocean, ice–atmosphere, and ice–bed boundaries. At the surface, observations show that reanalysis products underestimate air temperatures and melt, while regional climate models diverge significantly in their estimates of surface mass balance, underscoring the need for improved in situ data and models. At the ocean boundary, enhanced basal melting driven by both subglacial runoff and Atlantic water intrusions is identified as the dominant driver of recent mass loss of Petermann Glacier, with continued warming posing a serious threat to the stability of the floating tongue. At the bed, new geophysical synthesis reveals complex geology, likely spatial variability in geothermal heat flux, and the influence of the megacanyon on seasonal hydrology and velocity fluctuations. Petermann’s mass balance has been negative in recent decades without corresponding flow acceleration. However, the glacier has undergone significant calving events, and the current rifting that began in September 2025 highlights its vulnerability. This upcoming calving event underscores the timeliness of this review, as it will put Petermann Glacier’s terminus at its most retreated position since records began in 1923. The anticipated retreat of the ice tongue also reduces buttressing and brings the terminus closer to the grounding zone, and modeling studies suggest that calving within 12 km of the grounding zone could potentially trigger dynamic retreat, accelerating ice discharge, and a doubling of flow speeds. We conclude that improved observations, sustained monitoring of oceanographic and atmospheric properties, and high-resolution modeling are critical to constraining projections of Petermann Glacier’s future and its role in the stability of the Greenland Ice Sheet.

Dominik Fahrner↗

A New Method to Retrieve the Diurnal Variability of Planetary Boundary Layer Height from Lidar Under Different Thermodynamic Stability Conditions

The planetary boundary layer height (PBLH) is an important parameter for understanding the accumulation of pollutants and the dynamics of the lower atmosphere. Lidar has been used for tracking the evolution of PBLH by using aerosol backscatter as a tracer, assuming aerosol is generally well-mixed in the PBL; however, the validity of this assumption actually varies with atmospheric stability. This is demonstrated here for stable boundary layers (SBL), neutral boundary layers (NBL), and convective boundary layers (CBL) using an 8-year dataset of micropulse lidar (MPL) and radiosonde (RS) measurements at the ARM Southern Great Plains, and MPL at the GSFC site. Due to weak thermal convection and complex aerosol stratification, traditional gradient and wavelet methods can have difficulty capturing the diurnal PBLH variations in the morning and forenoon, as well as under stable conditions generally. A new method is developed that combines lidar-measured aerosol backscatter with a stability dependent model of PBLH temporal variation (DTDS). The latter helps “recalibrate” the PBLH in the presence of a residual aerosol layer that does not change in harmony with PBL diurnal variation. The hybrid method offers significantly improved PBLH detection, with better correlation and smaller biases, under most thermodynamic conditions, especially for SBL and CBL. Relying on the physical process of PBL diurnal development, different schemes are developed for growing, maintenance, and decaying periods. Comprehensive evaluation of this new method shows much better tracking of diurnal PBLH variation and significantly smaller biases under various pollution levels.

Tianning Su↗

Hypersonic Navier-Stokes Comparisons to Orbiter Flight Data

During the STS-119 flight of Space Shuttle Discovery, two sets of surface temperature measurements were made. Under the HYTHIRM program3 quantitative thermal images of the windward side of the Orbiter with a were taken. In addition, the Boundary Layer Transition Flight Experiment 4 made thermocouple measurements at discrete locations on the Orbiter wind side. Most of these measurements were made downstream of a surface protuberance designed to trip the boundary layer to turbulent flow. In this paper, we use the US3D computational fluid dynamics code to simulate the Orbiter flow field at conditions corresponding to the STS-119 re-entry. We employ a standard two-temperature, five-species finite-rate model for high-temperature air, and the surface catalysis model of Stewart.1 This work is similar to the analysis of Wood et al . 2 except that we use a different approach for modeling turbulent flow. We use the one-equation Spalart-Allmaras turbulence model8 with compressibility corrections 9 and an approach for tripping the boundary layer at discrete locations. In general, the comparison between the simulations and flight data is remarkably good

Candler, Graham V.↗

Impacts of Fully Coupling Land Surface and Flood Models on the Simulation of Large Wetlands’ Water Dynamics: The Case of the Inner Niger Delta

It is known that representing wetland dynamics in land surface modeling improves models ‘capacity to reproduce fluxes and land surface boundary conditions for atmospheric modeling in general circulation models. This study presents the development of the full coupling between the Noah-MP land surface model (LSM) and the HyMAP flood model in the NASA Land Information System and its application over the Inner Niger Delta (IND), a well-known hot-spot of strong land surface-atmosphere interactions in West Africa. Here, we define two experiments at 0.02o spatial resolution over 2002-2018 to quantify the impacts of the proposed developments on simulating IND dynamics. One represents the one-way approach for simulating land surface and flooding processes (1-WAY), i.e., Noah-MP neglects surface water availability, and the proposed two-way coupling (2-WAY), where Noah-MP takes surface water availability into account in the vertical water and energy balance. Results show that accounting for two-way interactions between Noah- MP and HyMAP over IND improves simulations of all selected hydrological variables. Compared to 1-WAY, evapotranspiration derived from 2-WAY over flooding zones doubles, increased by 0.8mm/day, resulting in an additional water loss rate of ~18,900km(exp 3)/year, ~40% drop of wetland extent during wet seasons and major improvement in simulated water level variability at multiple locations. Significant soil moisture increase and surface temperature drop were also observed. Wetland outflows decreased by 35%, resulting in a substantial a Nash-Sutcliffe coefficient improvement, from -0.73 to 0.79. It is anticipated that future developments in water monitoring and water-related disaster warning systems will considerably benefit from these findings.

Augusto Getirana↗

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

Murthy, V. R.↗

Computational fluid dynamic modeling to determine the indoor environment of an electron-ion collider service building

The design for the Electron-Ion Collider (EIC) calls for several service buildings that house various power supplies and control electronics for the collider ring itself. In order to operate within specified conditions, the ambient air entering the power supplies needs to be within a certain temperature range while dissipating the heat from losses. Proper cooling is therefore a necessity in the service buildings to ensure that every aspect of the EIC works as intended. Since the EIC is in the design stage, we are evaluating the indoor environment of the service building using the current design specifications. We have researched multiple forms of literature and performed the necessary calculations to compile a list of boundary conditions that accurately represent the situation at hand. We are using computational fluid dynamics modeling to solve the conservation equations for mass, momentum, and energy (Navier-Stokes). This allows us to perform a finite element analysis which will give us the flow distribution in the room as well as temperature profiles throughout the building. We have obtained a simulation result giving us the temperature profiles for the building and it shows that the placement of the racks and supply vents are essential to obtaining an even temperature distribution. This model will provide a basis for design decisions which will affect the overall cooling of the service building without extending the schedule and avoiding a costly reworking of the cooling system.

43 PARTICLE ACCELERATORS↗

Extended Lagrangian Born–Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models

We report extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) is formulated for orbital-free Hohenberg–Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born–Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗