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At least 703 records · Page 39

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NASA NTRS1982

Pilot model hypothesis testing

The aircraft control time history predicted by the optimal control pilot model and actual pilot tracking data obtained from NASA Langley's differential maneuvering simulator (DMS) are analyzed. The analysis is performed using a hypothesis testing scheme modified to allow for changes in the true hypothesis. A finite number of pilot models, each with different hypothesized internal model representations of the aircraft dynamics, are constructed. The hypothesis testing scheme determines the relative probability that each pilot model best matches the DMS data. By observing the changes in probabilities, it is possible to determine when the pilot changes control strategy and which hypothesized pilot model best represent's the pilot's control behavior.

Broussard, J. R.↗

NASA NTRS1996

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Zingg, David W.↗

NASA NTRS1983

High resolution applications of the Osher upwind scheme for the Euler equations

The 'Osher' scheme was introduced by Osher (1981). It represents an upwind finite-difference method for hyperbolic systems of conservation laws, including the Euler equations. In studies conducted by Osher (1981) and Osher and Solomon (1982), the method was applied to the nonisentropic form of the Euler equations in one dimension and the isentropically restricted form in two spatial dimensions, both in Cartesian coordinates. Chakravarthy and Osher (1982) have shown an approach for extending the Osher scheme to the Euler equations written for general geometries, taking into account the use of mappings to arbitrary curvilinear coordinate systems. The present investigation is concerned with the high resolution extension of the Osher scheme to second-order accuracy. Results are presented for several example problems, giving attention to quasi-one-dimensional Laval nozzle flow, a one-dimensional shock tube problem, and supersonic flow over a cylinder.

Chakravarthy, S. R.↗

DOE OSTI2019

A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations

We present a positive- and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on the well-known line source benchmark problem with the usual uniform material medium as well as a medium composed of different materials that are arranged in a checkerboard pattern. We also tested the scheme on a Riemann problem with a nonuniform material medium. The observed order of space-time accuracy of the proposed scheme is reported.

nite difference methods↗

NASA NTRS2004

Comparison of Numerical Schemes for a Realistic Computational Aeroacoustics Benchmark Problem

In this work, a nonlinear structured-multiblock CAA solver, the NASA GRC BASS code, will be tested on a realistic CAA benchmark problem. The purpose of this test is to ascertain what effect the high-accuracy solution methods used in CAA have on a realistic test problem, where both the mean flow and the unsteady waves are simultaneously computed on a fully curvilinear grid from a commercial grid generator. The proposed test will compare the solutions obtained using several finite-difference methods on identical grids to determine whether high-accuracy schemes have advantages for this benchmark problem.

Hixon, R.↗

NASA NTRS1987

A simple and efficient shear-flexible plate bending element

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Chaudhuri, Reaz A.↗

NASA NTRS1985

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Barth, T. J.↗

NASA NTRS1991

Use of finite volume schemes for transition simulation

The use of finite-volume methods in the study of spatially and temporally evolving transitional flows over a flat plate is investigated. Schemes are developed with both central and upwind differencing. The compressible Navier-Stokes equations are solved with a Runge-Kutta time stepping scheme. Disturbances are determined using linear theory and superimposed at the inflow boundary. Time accurate integration is then used to allow temporal and spatial disturbance evolution. Characteristic-based boundary conditions are employed. The requirements of using finite-volume algorithms are studied in detail. Special emphasis is placed on difference schemes, grid resolution, and disturbance amplitudes. Moreover, comparisons are made with linear theory for small amplitude disturbances. Both subsonic and supersonic flows are considered, and it is shown that the locations of branch 1 and branch 2 of the neutral stability curve are well predicted, given sufficient resolution.

Fenno, Charles C., Jr.↗

NASA NTRS1976

A note on the leap-frog scheme in two and three dimensions

The paper considers the leap-frog finite-difference method (Kreiss and Oliger, 1973) for systems of partial differential equations of the form du/dt = dF/dx + dG/dy + dH/dz, where d denotes partial derivative, u is a q-component vector and a function of x, y, z, and t, and the vectors F, G, and H are functions of u only. The original leap-frog algorithm is shown to admit a modification that improves on the stability conditions for two and three dimensions by factors of 2 and 2.8, respectively, thereby permitting larger time steps. The scheme for three dimensions is considered optimal in the sense that it combines simple averaging and large time steps.

Abarbanel, S.↗

NASA NTRS1985

A high-precision finite element method for shock-tube calculations

A two-pass explicit scheme is developed in order to exploit some of the capabilities of finite difference modeling (FDM) for finite element modeling (FEM), which offers the opportunity to account for any type of geometry in fluid flow modeling. Features of the first-order upwind and the Lax-Wendroff high precision explicit finite difference algorithms are reviewed. A flux limiter is developed for FEM to serve as an analog for the single limiter function which has been defined for the various FDMs. It is shown that an antidiffusive limiter must be introduced into the weighting function which normally multiplies the time-derivative term in the variational equation. The two-pass scheme which results is demonstrated to be the equivalent of FDMs with five-point support. However, the present scheme is valid only for one-dimensional calculations and linear shape functions for shock tube flow phenomena. Further work is required for its use with nonlinear hyperbolic systems.

Hughes, T. J. R.↗

DOE OSTI2017

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1976

Accelerated iterative calculation of transonic nacelle flowfields

A method is presented for the calculation of inviscid, supercritical flowfields about axisymmetric inlet cowls. A finite-difference calculation is performed in a simple, rectangular domain obtained from the nacelle geometry by a nearly-conformal mapping procedure. Type-dependent finite-differences are constructed using a coordinate-independent, 'rotated' differencing scheme. Methods of accelerating convergence of the iterative solution are demonstrated including a hybrid fast-Poisson-solver/relaxation scheme and an extrapolated relaxation procedure. Calculated pressure distributions are compared with experimental data for a variety of Mach numbers and mass-flow ratios, and show generally good agreement.

Caughey, D. A.↗

NASA NTRS1976

Advances in the application of fast semidirect computational methods in transonic flow

The paper uses finite-difference algorithms called 'fast direct elliptic solvers' within an iteration scheme for the rapid solution of the equations of inviscid transonic aerodynamics. The methods are called 'direct' (or semidirect) because the entire computational field is solved at once rather than in successive traverses over the field. These semidirect iterative methods have been limited here to the investigation of two-dimensional steady inviscid flow over airfoils in subsonic free stream.

Martin, E. D.↗

NASA NTRS1977

Turbulent plane Couette flow using probability distribution functions

A numerical scheme employing a combination of the discrete ordinate method and finite differences is developed for solving the one-dimensional form of Lundgren's (1967) model equation for turbulent plane Couette flow. The approach used requires no a priori assumption about the form of the turbulent distribution function, and the numerical solution is obtained directly from the governing differential equations. Two different types of boundary conditions (zero-gradient and Chapman-Enskog) for the distribution function are evaluated by comparing the numerical results with experimental data. It is found that: (1) the present approach gives convergent and stable results over a wide range of Reynolds numbers; (2) Lundgren's equation yields results that compare well with experimental data for mean velocity and skin friction in the case of simple Couette flow; (3) the zero-gradient boundary condition leads to a logarithmic flow profile; and (4) the Chapman-Enskog boundary condition provides very good agreement with experimental data when applied within the near-wall region.

Srinivasan, R.↗

NASA NTRS1979

A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

Weilmuenster, K. J.↗

NASA NTRS1983

A general perturbation approach for the equations of fluid dynamics

An efficient numerical technique to produce accurate solutions to the equations of fluid dynamics is presented where the governing equations are perturbed about an approximate solution and solved by finite-difference methods on a coarsened grid. The result is a scheme which substantially reduces the number of grid points necessary to accurately resolve the flow. Applications are presented for the two-dimensional Euler equations perturbed about a solution of the transonic full potential equation. However, the concept is applicable to arbitrary equation sets, higher dimensions and for a wide variety of applications.

Chow, L. J.↗

NASA NTRS1986

Interface procedures for overlapping grids

The solution of partial differential equations by means of either implicit or conservative explicit finite-difference methods, on the one hand, or multicomponent overlapping grid schemes on the other, is presently subjected to interpolation at grid boundaries in an attempt to eliminate the time lag. The accuracy of the transient solution of a hyperbolic or parabolic partial differential equation is dependent on the procedures used to transfer information between grids in a composite grid system. The present techniques reduce numerical solution errors.

Mastin, C. Wayne↗