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At least 811 records · Page 45

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NASA NTRS1993

Theory for noise of propellers in angular inflow with parametric studies and experimental verification

This report presents the derivation of a frequency domain theory and working equations for radiation of propeller harmonic noise in the presence of angular inflow. In applying the acoustic analogy, integration over the tangential coordinate of the source region is performed numerically, permitting the equations to be solved without approximation for any degree of angular inflow. Inflow angle is specified in terms of yaw, pitch, and roll angles of the aircraft. Since these can be arbitrarily large, the analysis applies with equal accuracy to propellers and helicopter rotors. For thickness and loading, the derivation is given in complete detail with working equations for near and far field. However, the quadrupole derivation has been carried only far enough to show feasibility of the numerical approach. Explicit formulas are presented for computation of source elements, evaluation of Green's functions, and location of observer points in various visual and retarded coordinate systems. The resulting computer program, called WOBBLE has been written in FORTRAN and follows the notation of this report very closely. The new theory is explored to establish the effects of varying inflow angle on axial and circumferential directivity. Also, parametric studies were performed to evaluate various phenomena outside the capabilities of earlier theories, such as an unsteady thickness effect. Validity of the theory was established by comparison with test data from conventional propellers and Prop Fans in flight and in wind tunnels under a variety of operating conditions and inflow angles.

Propeller acoustics↗

NASA NTRS1983

Numerical viscosity and the entropy condition for conservative difference schemes

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Tadmor, E.↗

NASA NTRS1984

Numerical viscosity and the entropy condition for conservative difference schemes

Tadmor, E.↗

NASA NTRS1984

Numerical simulation of boundary-layer transition

The transition to turbulence in boundary layers was investigated by direct numerical solution of the nonlinear, three-dimensional, incompressible Navier-Stokes equations in the half-infinite domain over a flat plate. Periodicity was imposed in the streamwise and spanwise directions. A body force was applied to approximate the effect of a nonparallel mean flow. The numerical method was spectra, based on Fourier series and Jacobi polynomials, and used divergence-free basis functions. Extremely rapid convergence was obtained when solving the linear Orr-Sommerfeld equation. The early nonlinear and three-dimensional stages of transition, in a boundary layer disturbed by a vibrating ribbon, were successfully simulated. Excellent qualitative agreement was observed with either experiments or weakly nonlinear theories. In particular, the breakdown pattern was staggered or nonstaggered depending on the disturbance amplitude.

Spalart, P. R.↗

DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements (≲100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1996

Numerical Algorithms Based on Biorthogonal Wavelets

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Ponenti, Pj.↗

NASA NTRS1996

Numerical Algorithms Based on Biorthogonal Wavelets

Ponenti, Pj.↗

NASA NTRS1947

Airfoil in sinusoidal motion in a pulsating stream

The forces and moments on a two-dimensional airfoil executing harmonic motions in a pulsating stream are derived on the basis of non-stationary incompressible potential flow theory, with the inclusion of the effect of the continuous sheet of vortices shed from the trailing edge. An assumption as to the form of the wake is made with a certain degree of approximation. A comparison with previous work applicable only to the special case of a stationary airfoil is made by means of a numerical example, and the excellent agreement obtained shows that the wake approximation is quite sufficient. The results obtained are expected to be useful in considerations of forced vibrations and flutter of rotary wing aircraft.

Greenberg, J Mayo↗

NASA NTRS1989

On the stability of Kuzmin/Toomre disks

A simple two-component system consiting of a Kuzmin/Toomre disk embedded in a spherically symmetrical 'halo' is studied with Plummer's density distribution. The bounds on the mass fraction of the disk component which result from applying the semiempirical criterion against bar instabilities due to Ostriker and Peebles are studied analytically and the results are compared with recent numerical simulations. It is found that the locus t = 0.14, calculated using analytic approximations for a variety of rotation laws, agrees reasonably well with the neutral stability line derived from numerical results.

Frank, Juhan↗

NASA NTRS1981

Experimental and numerical studies of the incompressible viscous flow over a two-dimensional airfoil

Physical and numerical experiments for the low Reynolds number flow over a two-dimensional NACA 66(3)-018 airfoil have been performed. Pressure distributions and smoke flow photographs have been obtained for a Reynolds number based on airfoil chord and free-stream conditions of approximately 40,000 at angles of attack of 0 and 6 deg, and for a Reynolds number based on airfoil chord and free-stream conditions of approximately 400,000 at angles of attack of 0 and 12 deg in a low turbulence wind tunnel. Finite difference numerical experiments, using an approximate factorization method, have been obtained for a Reynolds number of 40,000 at angles of attack of 0 and 6 deg. Although the comparison of the wind tunnel and computer results is encouraging, further studies of this type are clearly necessary.

Mueller, T. J.↗

NASA NTRS1991

The energy decay in self-preserving isotropic turbulence revisited

The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup - alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state towards which a complete self-preseving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.

Speziale, Charles G.↗

DOE OSTI2021

Numerical solution of singular Lyapunov equations

We consider the numerical solution of large scale singular (continuous-time) Lyapunov equations of the form AX + XA T + BB T = 0, where A is semistable, that is, its spectrum is contained in the left half plane, with the exception of a few semisimple eigenvalues at zero. We also consider the case of a few semisimple eigenvalues on the imaginary axis. We assume that we know these few eigenvalues (zero or imaginary), and that we have or can compute the corresponding invariant subspaces. We use this information to build an appropriate newly proposed subspace on which to project the Lyapunov equations, and then compute a low-rank approximation to the least squares solution. Selected illustrative numerical examples are provided.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

Numerical experiments on the theta pinch

Numerical calculation of theta pinch problems are presented. Physical processes in theta pinch systems are considered in a one dimensional, two temperature magnetohydrodynamic, approximation with allowance for end losses by longitudinal heat conductivity. The numerical calculations are compared with results of earlier experiments.

Volosevich, P. P.↗

DOE OSTI2022

Forward and inverse modeling of fault transmissibility in subsurface flows

Characterizing physical properties of faults, such as their transmissibility, is crucial for performing predictive numerical simulation of subsurface flows, such as those encountered in petroleum engineering and remediation of subsurface contamination. Here, this paper provides a complete investigation of the inverse problem for fault transmissibility in subsurface flow models, under appropriate assumptions on fault structure. In particular, the following aspects are considered: 1) fault modeling and well-posedness of the forward problem; 2) finite element (FEM) discretizations of the forward problem and their rigorous a priori convergence analysis; 3) Well-posedness of the Bayesian inverse problem, FEM discretization of the infinite dimensional Bayesian inverse formulation, and its rigorous a priori analysis. Moreover, computation of the maximum a posteriori (MAP) point via fast inexact Newton-conjugate gradient optimization and a Laplace approximation of the Bayesian posterior are also presented. Numerical results illustrate the use of the proposed fault model in forward and inverse problems for subsurface flows in two dimensional domains with multiple faults.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1995

The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems

A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.

Chang, Sin-Chung↗

NASA NTRS1985

Bounds and approximations for rapid evaluation of coherent MPSK error probabilities

The error probability for MPSK detection is expressed here as a sum of a familiar upper-bound approximation and a correction term which is well suited for numerical integration. An asymptotic expansion of the correction term is derived, from which simple and extremely tight upper and lower bounds are obtained. Relative errors in using these bounds and approximations of them are graphed for cases of practical interest.

Chie, C. M.↗

NASA NTRS1989

Evolution of cosmic string networks

Results on cosmic strings are summarized including: (1) the application of non-equilibrium statistical mechanics to cosmic string evolution; (2) a simple one scale model for the long strings which has a great deal of predictive power; (3) results from large scale numerical simulations; and (4) a discussion of the observational consequences of our results. An upper bound on G mu of approximately 10(-7) emerges from the millisecond pulsar gravity wave bound. How numerical uncertainties affect this are discussed. Any changes which weaken the bound would probably also give the long strings the dominant role in producing observational consequences.

Albrecht, Andreas↗