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The aim of the present research program is the development of more efficient and reliable calculation schemes for the coupled momentum and continuity equations. The resulting schemes would significantly reduce the expense of computing complex flows such as those in combustion chambers, gas turbines, and heat exchangers.
The use of canards in advanced aircraft for control and improved aerodynamic performance is a topic of continued interest and research. In addition to providing maneuver control and trim, the influence of canards on wing aerodynamics can often result in increased maximum lift and decreased trim drag. In many canard-configured aircraft, the main benefits of canards are realized during maneuver or other dynamic conditions. Therefore, the detailed study and understanding of canards requires the accurate prediction of the non-linear unsteady aerodynamics of such configurations. For close-coupled canards, the unsteady aerodynamic performance associated with the canard-wing interaction is of particular interest. The presence of a canard in close proximity to the wing results in a highly coupled canard-wing aerodynamic flowfield which can include downwash/upwash effects, vortex-vortex interactions and vortex-surface interactions. For unsteady conditions, these complexities of the canard-wing flowfield are further increased. The development and integration of advanced computational technologies provide for the time-accurate Navier-Stokes simulations of the steady and unsteady canard-wing-body flox,fields. Simulation, are performed for non-linear flight regimes at transonic Mach numbers and for a wide range of angles of attack. For the static configurations, the effects of canard positioning and fixed deflection angles on aerodynamic performance and canard-wing vortex interaction are considered. For non-static configurations, the analyses of the canard-wing body flowfield includes the unsteady aerodynamics associated with pitch-up ramp and pitch oscillatory motions of the entire geometry. The unsteady flowfield associated with moving canards which are typically used as primary control surfaces are considered as well. The steady and unsteady effects of the canard on surface pressure integrated forces and moments, and canard-wing vortex interaction are presented in detail including the effects of the canard on the static and dynamic stability characteristics. The current study provides an understanding of the steady and unsteady canard-wing-body flowfield. Emphasis is placed on the effects of the canard on aerodynamic performance as well as the detailed flow physics of the canard-wing flowfield interactions. The computational tools developed to accurately predict the time-accurate flowfield of moving canards provides for the capability of coupled fluids-controls simulations desired in the detailed design and analysis of advanced aircraft.
CFD calculations using the Reynolds-averaged Navier-Stokes equations coupled with species continuity equations have been made for a supersonic coaxial-jet CFD-validation experiment to determine the sensitivity of the external flowfield to the main-nozzle exit profile. Four different nozzle exit profiles were used in the study: a uniform profile, one computed using only the nozzle geometry, one computed using the nozzle geometry and part of the upstream facility combustor, and one using the nozzle and the full facility combustor. Two cases were examined using the four profiles: a non-reacting case without coflow and a reacting case with hydrogen coflow. Results show that the nozzle exit profile has a significant effect on the external flowfield. The uniform profile produced the longest jet while the profile created with the full combustor produced the shortest jet. The nozzle-only and part-combustor profiles fell between the other two profiles. The reacting flow was found to be more sensitive to the nozzle exit profile since it affects the downstream mixing and combustion. These calculations indicate the importance of properly setting the nozzle-exit profile for this type of calculation.
While the dominant focus on short response missions has appropriately centered on the launch vehicle and spacecraft, often overlooked or afterthought phases of these missions have been launch site operations and the activities of launch range organizations. Throughout the history of organized spaceflight, launch ranges have been the bane of flight programs as the source of expense, schedule delays, and seemingly endless requirements. Launch Ranges provide three basic functions: (1) provide an appropriate geographical location to meet orbital other mission trajectory requirements, (2) provide project services such as processing facilities, launch complexes, tracking and data services, and expendable products, and (3) assure safety and property protection to participating personnel and third-parties. The challenge with which launch site authorities continuously struggle, is the inherent conflict arising from projects whose singular concern is execution of their mission, and the range s need to support numerous simultaneous customers. So, while tasks carried out by a launch range committed to a single mission pale in comparison to efforts of a launch vehicle or spacecraft provider and could normally be carried out in a matter of weeks, major launch sites have dozens of active projects separate sponsoring organizations. Accommodating the numerous tasks associated with each mission, when hardware failures, weather, maintenance requirements, and other factors constantly conspire against the range resource schedulers, make the launch range as significant an impediment to responsive missions as launch vehicles and their cargo. The obvious solution to the launch site challenge was implemented years ago when the Department of Defense simply established dedicated infrastructure and personnel to dedicated missions, namely an Inter Continental Ballistic Missile. This however proves to be prohibitively expensive for all but the most urgent of applications. So the challenge becomes how can a launch site provide acceptably responsive mission services to a particular customer without dedicating extensive resources and while continuing to serve other projects? NASA's Wallops Flight Facility (WFF) is pursuing solutions to exactly this challenge. NASA, in partnership with the Virginia Commercial Space Flight Authority, has initiated the Rapid Response Range Operations Initiative (R3Ops). R3Ops is a multi-phased effort to incrementally establish and demonstrate increasingly responsive launch operations, with an ultimate goal of providing ELV-class services in a maximum of 7-10 days from initial notification routinely, and shorter schedules possible with committed resources. This target will be pursued within the reality of simultaneous concurrent programs, and ideally, largely independent of specialized flight system configurations. WFF has recently completed Phase 1 of R3Ops, an in-depth collection (through extensive expert interviews) and software modeling of individual steps by various range disciplines. This modeling is now being used to identify existing inefficiencies in current procedures, to identify bottlenecks, and show interdependencies. Existing practices are being tracked to provide a baseline to benchmark against as new procedures are implemented. This paper will describe in detail the philosophies behind WFF's R3Ops, the data collected and modeled in Phase 1, and strategies for meeting responsive launch requirements in a multi-user range environment planned for subsequent phases of this initiative.
Abstract We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.
In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC
The standard particle-in-cell (PIC) method employs explicit finite-difference (FD) methods (e.g. the leap-frog scheme) for both spatial and temporal integrations. Here, we employ a pseudospectral method for solving the Poisson equation and a fully implicit time integration to achieve exact energy conservation. The advantage of a pseudospectral field solver is its spectral accuracy in solving field solutions. Earlier studies of implicit time integration of PIC FD equations can enforce exact energy exchange between field and particles, resulting in exact energy-conserving schemes. Here, we prove that the exact energy conservation property can be carried over to the pseudospectral scheme. Simultaneously, we provide a solution to ensure a pseudospectral charge continuity equation. We demonstrate the new scheme in a 2D electrostatic PIC code. In conclusion, theoretical results are confirmed via numerical examples.
We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.
Moore’s Law is a techno-economic model that has enabled the information technology industry to double the performance and functionality of digital electronics roughly every 2 years within a fixed cost, power and area. Advances in silicon lithography have enabled this exponential miniaturization of electronics, but, as transistors reach atomic scale and fabrication costs continue to rise, the classical technological driver that has underpinned Moore’s Law for 50 years is failing and is anticipated to flatten by 2025. Here, this article provides an updated view of what a post-exascale system will look like and the challenges ahead, based on our most recent understanding of technology roadmaps. It also discusses the tapering of historical improvements, and how it affects options available to continue scaling of successors to the first exascale machine. Lastly, this article covers the many different opportunities and strategies available to continue computing performance improvements in the absence of historical technology drivers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.
SAND2023-06647O The latest version of the CTH suite of computer codes is a flexible software system designed to treat a wide range of shock wave propagation and material motion phenomena in 1-D, 2-D, or 3-D. CTH has models suitable for most conditions encountered in shock physics including material strength, fracture, distended materials, high explosives, and a variety of boundary conditions. Finite-volume analogs of the Lagrangian equations of momentum and energy conservation are employed with continuous rezoning to construct Eulerian differencing. Adaptive mesh refinement is available for maximizing resolution in regions of interest. Full Lagrangian numerical methods are available for mechanical or structural response.
Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.
Tests were conducted to determine the experimental pressure drop and velocity data for water flowing through woven screens. The types of materials used are dutch twill and square weave fabrics. Pressure drop measures were made at four locations in a rectangular channel. The data are presented as change in pressure compared with the average entry velocity and the numerical relationship is determined by dividing the volumetric flow rate by the screen area open to flow. The equations of continuity and momentum are presented. A computer program listing an extension of a theoretical model and data from that computer program are included.
Na2SO4(l)-NaCl(g) interactions were studied at a total pressure of one atmosphere of air or oxygen for various temperatures of Na2SO4(l) and for various partial pressures of NaCl(g) and H2O(g). Mass spectrometric sampling techniques were used to identify and monitor gas phase species. Continuous recording thermomicrogravimetric measurements were conducted to determine condensed phase weight change rates. Experimental measurements were supplemented with thermodynamic calculations. Numerous experiments were performed at sample temperatures of 900 and 1000 C with 300 ppm NaCl(g). In these experiments, the reproducibility of the Na2SO4 vaporization weight loss rate and initial weight gain upon addition of NaCl(g) were found to be satisfactory. It was found that the addition of NaCl(g) to air flowing over Na2SO4(l) at 900 and 1000 C enhances the rate of weight loss of the Na2SO4(l). This enhancement increases when H2O(g) is also added to the air flow.
The relationship between the pattern of plasma convection in the polar cleft and the dynamics of the interplanetary electric field (IEF) is examined theoretically. It is shown that owing to the geometrical properties of the magnetosphere, the East-West component of the IEF will drive field-aligned currents which connect to the ionosphere at points lying on either side of noon, while currents associated with the North-South component of the IEF will connect the two polar caps as sheet currents, also centered at 12 MLT. In order to describe the consequences of the Interplanetary Magnetic Field (IMF) effects upon high-latitude electric fields and convection patterns, a series of numerical simulations was carried out. The simulations were based on a solution to the steady-state equation of current continuity in a height-integrated ionospheric current. The simulations demonstrate that a simple hydrodynamical model can account for the narrow 'throats' of strong dayside antisunward convection observed during periods of southward interplanetary IMF drift, as well as the sunward convection observed during periods of strongly northward IMF drift.
By using metallic glass compositions with a high relative glass transition temperature, such as Pd40Ni40P20, homogeneous nucleation also becomes negligible. Large (5g) masses of this alloys were obtained using a molten B2O3 flux. Presently, bulk glass formation in iron based glasses is being investigated. It is expected that if an undercooling of about 250K can be achieved in a Ge or Si melt, formation of the amorphous semiconductor phase (rather than the crystal) may be kinetically favored. The volumetric behavior of undercooled liquid Ga droplet dispersion is investigated by dilatometry. A theoretical model (both analytical and numerical) was developed for transient nucleation in glass forming melts. The model, originally designed for isothermal conditions, was extended to continuous quenching. It is being applied to glass formation in various metallic and oxide systems. A further refinement will be the inclusion of diffusion controlled interfacial rearrangements governing the growth of the crystal embryos.
Numerical solutions from the time-steady viscous shock-layer equations are presented for the hypersonic laminar and turbulent flow of a perfect gas over long slender bodies. These results are obtained from a spatial-marching implicit finite-difference technique. Detailed comparisons have been made with other predictions and experimental data to assess the accuracy of the present numerical technique, especially for slender-body flows. Results from the present method show that coupling the normal momentum and continuity equations and the use of the Vigneron pressure condition in the subsonic nose region give quite accurate and stable results. These results compare (with some exceptions) favorably with those obtained using PNS and other VSL methods.
Transient cooling was analyzed for a two-dimensional gray rectangular region that emits, absorbs, and isotropically scatters radiation. The region, initially at uniform temperature, is placed in surroundings at a much lower temperature. The cooling analysis yields two simultaneous equations for the transient temperature and scattering source function distributions. The region starts to cool with the medium at uniform temperature. For this condition, the local emittance around the perimeter was obtained by a numerical solution of the radiative equations, and the rate of heat loss from the entire medium was evaluated. As cooling continues, the emissive ability decreases because of the lower temperatures in the outer regions of the rectangle. Based on some previous work, a lower limit for the transient overall emittance was found by obtaining a similarity solution. For some ranges of optical thickness and scattering albedo, the lower limit is only a small amount below the initial emittance. For these conditions, the initial emittance can be used to compute the entire transient resulting in a considerable simplification.