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At least 91 records · Page 5

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DOE OSTI2022

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A Design Method for Low-Pressure Venturi Nozzles

The purpose of this work is to provide empirical design models for low-pressure, subsonic Venturi nozzles. Experimentally validated simulations were used to determine the effect of nozzle geometry and operating conditions on the suction ratio (ratio of suction mass flow rate to motive mass flow rate) of low-pressure, subsonic Venturi nozzles, over a wide range of geometries and operating conditions, through a parametric study. The results of the parametric study were used to develop seven empirical models, each with a different range of applicability or calculating a different indicator of nozzle performance (i.e., suction ratio, momentum ratio, or dynamic pressure ratio), of the Venturi nozzles using a constrained multi-variable global optimization method. Of the seven empirical models, the best models were found to be those for low- (less than one) and high-suction ratios (greater than one), with mean absolute percentage errors of 5% and 18%, respectively. These empirical models provide a design tool for subsonic, low-pressure Venturi nozzles that is more than an order of magnitude more accurate than a governing equation approach or conventional flow head calculations. These newly-developed empirical models can be applied for initial nozzle design when precise suction ratios are required.

O’Hern, Hannah↗

NASA NTRS1972

Evaluating foam heterogeneity

New analytical tool is available to calculate the degree of foam heterogeneity based on the measurement of gas diffusivity values. Diffusion characteristics of plastic foam are described by a system of differential equations based on conventional diffusion theory. This approach saves research and computation time in studying mass or heat diffusion problems.

Liou, D. W.↗

NASA NTRS1977

Analytical study of viscous effects on transonic flow over boattail nozzles

An analytical study has been made of the effects of viscous/inviscid interactions on the transonic flow over boattail nozzles. The theoretical method couples a relaxation solution of the full potential transonic flow equations with a conventional boundary-layer solution to account for displacement-thickness effects. Surface pressures calculated on circular-arc boattails with solid jet-plume simulators show good agreement with experiment for free-stream Mach numbers less than 0.90. For separated flows, an empirical discriminating streamline model of the separation bubble gives good results until the onset of shock-induced separation, which occurs typically at a Mach number of about 0.90.

Wilmoth, R. G.↗

NASA NTRS1979

Preferential spectral transport by irrotational straining

The addition of an extra term to the conventional approximate transport equation for the turbulence energy dissipation rate is recommended. The term may be viewed as emphasizing the role of irrotational deformations in promoting energy transfer across the spectrum or, equivalently, as augmenting the influence of normal strains. Calculations including the new term are reported for the plane and round jet and for several turbulent boundary layers. In the cases considered the addition of the new term significantly improves agreement with experimental data.

Hanjalic, K.↗

NASA NTRS1995

Convergence acceleration of the Proteus computer code with multigrid methods

This report presents the results of a study to implement convergence acceleration techniques based on the multigrid concept in the two-dimensional and three-dimensional versions of the Proteus computer code. The first section presents a review of the relevant literature on the implementation of the multigrid methods in computer codes for compressible flow analysis. The next two sections present detailed stability analysis of numerical schemes for solving the Euler and Navier-Stokes equations, based on conventional von Neumann analysis and the bi-grid analysis, respectively. The next section presents details of the computational method used in the Proteus computer code. Finally, the multigrid implementation and applications to several two-dimensional and three-dimensional test problems are presented. The results of the present study show that the multigrid method always leads to a reduction in the number of iterations (or time steps) required for convergence. However, there is an overhead associated with the use of multigrid acceleration. The overhead is higher in 2-D problems than in 3-D problems, thus overall multigrid savings in CPU time are in general better in the latter. Savings of about 40-50 percent are typical in 3-D problems, but they are about 20-30 percent in large 2-D problems. The present multigrid method is applicable to steady-state problems and is therefore ineffective in problems with inherently unstable solutions.

Demuren, A. O.↗

NASA NTRS1994

A mapping method for the gravitational few-body problem with dissipation

Recently a new class of numerical integration methods - 'mixed variable symplectic integrators' - has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of magnitude faster than conventional ordinary differential equations (ODE) integration methods. Here we present a simple modification of this method to include small non-gravitational forces. The new scheme provides a similar advantage of computational speed for a larger class of problems in Solar System dynamics.

Malhotra, Renu↗

NASA NTRS1994

Optimizations on Designing High-Resolution Finite-Difference Schemes

We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.

Liu, Yen↗

NASA NTRS2005

Investigation of Compressibility Effect for Aeropropulsive Shear Flows

Rocket Based Combined Cycle (RBCC) engines operate within a wide range of Mach numbers and altitudes. Fundamental fluid dynamic mechanisms involve complex choking, mass entrainment, stream mixing and wall interactions. The Propulsion Research Center at the University of Alabama in Huntsville is involved in an on- going experimental and numerical modeling study of non-axisymmetric ejector-based combined cycle propulsion systems. This paper attempts to address the modeling issues related to mixing, shear layer/wall interaction in a supersonic Strutjet/ejector flow field. Reynolds Averaged Navier-Stokes (RANS) solutions incorporating turbulence models are sought and compared to experimental measurements to characterize detailed flow dynamics. The effect of compressibility on fluids mixing and wall interactions were investigated using an existing CFD methodology. The compressibility correction to conventional incompressible two- equation models is found to be necessary for the supersonic mixing aspect of the ejector flows based on 2-D simulation results. 3-D strut-base flows involving flow separations were also investigated.

Balasubramanyam, M. S.↗

DOE OSTI2024

CO 2 rock physics modeling for reliable monitoring of geologic carbon storage

Monitoring, verification, and accounting (MVA) are crucial to ensure safe and long-term geologic carbon storage. Seismic monitoring is a key MVA technique that utilizes seismic data to infer elastic properties of CO 2 -saturated rocks. Reliable accounting of CO 2 in subsurface storage reservoirs and potential leakage zones requires an accurate rock physics model. However, the widely used CO 2 rock physics model based on the conventional Biot-Gassmann equation can substantially underestimate the influence of CO 2 saturation on seismic waves, leading to inaccurate accounting. We develop an accurate CO 2 rock physics model by accounting for both effects of the stress dependence of seismic velocities in porous rocks and CO 2 weakening on the rock framework. We validate our CO 2 rock physics model using the Kimberlina-1.2 model (a previously proposed geologic carbon storage site in California) and create time-lapse elastic property models with our new rock physics method. We compare the results with those obtained using the conventional Biot-Gassmann equation. Our innovative approach produces larger changes in elastic properties than the Biot-Gassmann results. Using our CO 2 rock physics model can replicate shear-wave speed reductions observed in the laboratory. Our rock physics model enhances the accuracy of time-lapse elastic-wave modeling and enables reliable CO 2 accounting using seismic monitoring.

58 GEOSCIENCES↗

NASA NTRS1987

Incompressible Navier-Stokes solutions for a sharp-edged double-delta wing

An implicit finite-difference scheme is used to compute the incompressible laminar vortical flow around a double-delta wing with an aspect ratio of 2.06. By adding a time derivative of the pressure to the continuity equation, the unsteady incompressible Navier-Stokes equations can be integrated like a conventional parabolic time-dependent system of equations. The flux-difference split scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The trajectory of the vortical core is well predicted in comparison with experimental data.

Hsu, Chung-Hao↗

DOE OSTI2023

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations—usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. Furthermore, the resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

Numerical solution of differential equations by artificial neural networks

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Meade, Andrew J., Jr.↗

NASA NTRS1971

Development of control systems for space shuttle vehicles. Volume 2: Appendixes

A launch phase random normal wind model is presented for delta wing, two-stage, space shuttle control system studies. Equations, data, and simulations for conventional launch studies are given as well as pitch and lateral equations and data for covariance analyses of the launch phase of MSFC vehicle B. Lateral equations and data for North American 130G and 134D are also included along with a high-altitude abort simulation.

Stone, C. R.↗

NASA NTRS1991

Progress in the development of PDF turbulence models for combustion

A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.

Hsu, Andrew T.↗

NASA NTRS1985

Confined swirling jet predictions using a multiple-scale turbulence model

A recently developed multiple scale turbulence model is used for the numerical prediction of isothermal, confined turbulent swirling flows. Because of the streamline curvature and nonequilibrium spectral energy transfer nature of the swirling flow, the utilized multiple scale turbulence model includes a different set of response equations for each of the large scale energetic eddies and the small scale transfer eddies. Predictions are made of a confined coaxial swirling jet in a sudden expansion and comparisons are made with experimental data and with the conventional single scale two equation model. The multiple scale model shows significant improvement of predictions of swirling flows over the single scale k epsilon model. The sensitivity study of the effect of prescribed inlet turbulence levels on the flow fields is also included.

Chen, C. P.↗

NASA NTRS1995

A new angle on the Euler angles

We present a generalization of the Euler angles to axes beyond the twelve conventional sets. The generalized Euler axes must satisfy the constraint that the first and the third are orthogonal to the second; but the angle between the first and third is arbitrary, rather than being restricted to the values 0 and pi/2, as in the conventional sets. This is the broadest generalization of the Euler angles that provides a representation of an arbitrary rotation matrix. The kinematics of the generalized Euler angles and their relation to the attitude matrix are presented. As a side benefit, the equations for the generalized Euler angles are universal in that they incorporate the equations for the twelve conventional sets of Euler angles in a natural way.

Markley, F. Landis↗

NASA NTRS1988

Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

Ng, C. K.↗