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At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Canonical and noncanonical Hamiltonian operator inference

Here, a method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Influence of nonconservative differencing on transonic streamline shapes

A computer program recently developed by South and Brandt (1976) which contained the Murman (1973) conservative finite-difference scheme is easily modified to use the Garabedian and Korn (1971) nonconservative finite difference scheme. This program solves the transonic small disturbance equation for only symmetric flow, but incorporates several iterative solution techniques. Results are presented for the case where the equally spaced computational grid extended to infinity in both the streamwise and normal directions. Streamline shapes are obtained along several grid lines by a streamwise integration of the normal component of the perturbation velocity. Comparison cases are run for a 10% thick parabolic arc airfoil at zero incidence for freestream Mach numbers of 0, 0.70, 0.84, and 0.95. It is shown that the use of a nonconservative finite-difference scheme in transonic flow calculations destroys the global mass balance when shocks are present. This lack of mass balance may prove to be more crucial in the case of an unconfined external flow.

Newman, P. A.↗
NASA NTRS1978

Discrepancy in proton flux extrapolation along field lines in the middle Jovian magnetosphere

Fluxes of energetic electrons and protons in Jupiter's outer magnetosphere were observed to be modulated with the 10 hour rotation period of the planet. This modulation was due to the concentration of particles at the magnetic equator: the non-alignment of Jupiter's spin and rotation axes caused Pioneer-10 to oscillate between +20 deg and -19 deg magnetic latitude and hence, between regions of stronger and weaker fluxes. The relationship between electron and proton fluxes observed off the magnetic equator was countered with measurements at the equatorial crossing radii of the same flux tubes by applying Liouville's theorem with the assumption that particles move conserving their magnetic moments. A magnetic model which matches the intensity and direction of the magnetic field along the Pioneer 10 trajectory was used for determining the positions of the equatorial crossings. Energetic electrons compared in this way appear to be consistently described. Protons, on the other hand, show much weaker fluxes at the off-equatorial points than would be predicted by this simple application of Liouville's theorem.

Schardt, A. W.↗
NASA NTRS1983

Design of shock-free compressor cascades including viscous boundary layer effects

A computer code that generates shock-free transonic compressor cascade shapes while taking into account viscosity effects is developed. The mathematical model for the inviscid flow field is the full potential equation. The Kutta-Joukowski condition is satisfied by varying the free stream angle at downstream infinity. A boundary fitted computational grid of C-type is generated using a sequence of conformal mapping and nonorthogonal coordinate stretching and shearing transformations. The inviscid calculation is performed sequentially on up to four consecutively refined grids thereby accelerating the convergence of the solution process. The full potential equation is solved using a finite area technique and rotated, type-dependent finite differencing. Artificial viscosity of the first order is added in a fully conservative form. Shock-free cascade airfoil shapes are obtained using the fictitious gas concept of Sobieczky and the method of characteristics in the rheograph plane. Viscosity effects are incorporated via a boundary layer displacement thickness. The integral boundary layer code is based on Rotta's turbulence model and assumes transition region of zero length.

Dulikravich, G. S.↗
NASA NTRS1986

Computation of separated flow on a ramp using the space marching conservative supra-characteristics method

Steady, hypersonic viscous flows over compression corners with streamwise separation have been computed using the space marching Conservative Supra-Characteristics Method (CSCM-S) of Lombard. The CSCM-S method permits stable space marching of the parabolized Navier-Stokes (PNS) equations through large separated flow regions. The present method has been used to compute surface pressure, heat transfer, and skin friction coefficients for two compression corner cases studied experimentally by Holden and Moselle. The computed results compare favorably with previous Navier-Stokes results and the experimental data. The present method has also been compared with the conventional Beam-Warming scheme for solving the PNS equations. Comparison are made for accuracy, computer time, and computer storage.

Stookesberry, D. C.↗
NASA NTRS1989

Improved vortex methods for three-dimensional flows

Robust numerical methods are developed for three-dimensional incompressible vortical flows, using Lagrangian vortex elements. A successful scheme must be able to handle regions of intense vortex stretching and vortex reconnection with reasonable accuracy (without diverging). Here, consideration is given to vortex particles, also commonly called vortons or vortex sticks. The following issues are discussed: (1) use of delta-function elements and weak solutions of the vorticity equation; (2) use of smoothed elements and the choice of the smoothing function; (3) representation of viscous effects and the redistribution of element strength; and (4) conservation laws (are they satisfied?). The various proposed schemes have been tested on flows involving a strong interaction between two vortex rings.

Winckelmans, G.↗
NASA NTRS1994

Effects of spatial order of accuracy on the computation of vortical flowfields

The objective of the present investigation is to assess the effect of the spatial order of accuracy used for the evaluation of the inviscid fluxes on the resolution of higher order quantitites, such as velocity gradients. The viscous terms are computed as second-order accurate with central difference formulas, even though for the explicit part of the algorithm higher order approximations may be used. A viscous/inviscid method is used, and the outer part of the flowfield is computed with the inviscid flow equations. The viscous boundary-layer type flow region close to the body surface is computed with an algebraic eddy viscosity model. Results obtained with the conservative and nonconservative formulations and the viscous/inviscid approach are compared with available experimental data. The effect of grid refinement on the accuracy of the solution is also presented.

Ekaterinaris, J. A.↗
NASA NTRS1998

A Preliminary Model Study of the Large-Scale Seasonal Cycle in Bottom Pressure Over the Global Ocean

Output from the primitive equation model of Semtner and Chervin is used to examine the seasonal cycle in bottom pressure (Pb) over the global ocean. Effects of the volume-conserving formulation of the model on the calculation Of Pb are considered. The estimated seasonal, large-scale Pb signals have amplitudes ranging from less than 1 cm over most of the deep ocean to several centimeters over shallow, boundary regions. Variability generally increases toward the western sides of the basins, and is also larger in some Southern Ocean regions. An oscillation between subtropical and higher latitudes in the North Pacific is clear. Comparison with barotropic simulations indicates that, on basin scales, seasonal Pb variability is related to barotropic dynamics and the seasonal cycle in Ekman pumping, and results from a small, net residual in mass divergence from the balance between Ekman and Sverdrup flows.

Ponte, Rui M.↗
NASA NTRS2005

A Robust Absorbing Boundary Condition for Compressible Flows

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

Loh, Ching Y.↗
NASA NTRS2011

Failure Assessment Diagram for Titanium Brazed Joints

The interaction equation was used to predict failure in Ti-4V-6Al joints brazed with Al 1100 filler metal. The joints used in this study were geometrically similar to the joints in the brazed beryllium metering structure considered for the ATLAS telescope. This study confirmed that the interaction equation R(sub sigma) + R(sub Tau) = 1, where R(sub sigma) and R(sub Tau)are normal and shear stress ratios, can be used as conservative lower bound estimate of the failure criterion in ATLAS brazed joints as well as for construction of the Failure Assessment Diagram (FAD).

Flom, Yury↗
NASA NTRSDate not supplied

Edge Based Viscous Method for Node-Centered Formulations

This paper presents a novel, efficient, conservative, edge-based method for evaluation of mean flow viscous fluxes and turbulence-model diffusion terms of the Reynolds-averaged Navier-Stokes equations on tetrahedral grids. The new method is implemented in a practical, node-centered, finite-volume computational fluid dynamics solver. The baseline finite-volume scheme that is equivalent to a second-order accurate finite-element Galerkin approximation of viscous stresses is reformulated. The order of operations to compute the cell-based Green-Gauss gradients is changed to combine the operations by edge, which leads to an equivalent formulation on tetrahedral grids, improves efficiency, and preserves the compact discretization stencil based on the nearest neighbors. The computational results presented in this paper verify the implementation of this edge-based method by comparing its accuracy and iterative convergence with those of the well verified and validated baseline formulation. Efficiency gains for residual and Jacobian evaluations result in significant reduction of time to solution. This novel edge-based formulation on tetrahedra can be seamlessly combined with the baseline formulation on cells of other types for computing solutions on mixed-element grids.

Edge Based↗
NASA NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
NASA NTRS2007

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.

Farassat, F.↗
NASA NTRS1994

Energy and maximum norm estimates for nonlinear conservation laws

We have devised a technique that makes it possible to obtain energy estimates for initial-boundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)(sub x), and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as point wise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm.

Olsson, Pelle↗
DOE OSTI2023

Detectability of subsolar mass neutron stars through a template bank search

Here, we study the detectability of gravitational-wave signals from subsolar-mass binary neutron star systems by the current generation of ground-based gravitational-wave detectors. We find that finite size effects from large tidal deformabilities of the neutron stars and lower merger frequencies can significantly impact the sensitivity of the detectors to these sources. By simulating a matched-filter based search using injected binary neutron star signals with tidal deformabilities derived from physically motivated equations of state, we calculate the reduction in sensitivity of the detectors. We conclude that the loss in sensitive volume can be as high as 78.4% for an equal mass binary system of chirp mass 0.17M ⊙ , in a search conducted using binary black hole template banks. We use this loss in sensitive volume, in combination with the results from the search for subsolar-mass binaries conducted on data collected by the LIGO-Virgo observatories during their first three observing runs, to obtain a conservative upper limit on the merger rate of subsolar-mass binary neutron stars. Since the discovery of a low-mass neutron star would provide new insight into formation mechanisms of neutron stars and further constrain the equation of state of dense nuclear matter, our result merits a dedicated search for subsolar-mass binary neutron star signals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗