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Results for “Iterative methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Iterative solution of transonic flows over airfoils and wings, including flows at Mach 1

A new method of calculating transonic flows based on a 'rotated' difference scheme is described. It is suitable for the calculation of both two- and three-dimensional flows without restriction on the speed at infinity and is well adapted to computer use. The Murman procedure is modified to eliminate any assumptions about the direction of flow when constructing the difference scheme. The proper directional property is obtained by rotating the difference scheme to conform with the local stream direction. In the hyperbolic region retarded difference formulas are used for all contributions to the streamwise second derivative, producing a correctly oriented positive artificial viscosity. In the absence of a simple implicit scheme in the hyperbolic and elliptic regions, the concept of iterations as steps in artificial time is introduced. Computer testing of this procedure provides numerical confirmation of the existence and uniqueness of weak solutions of the potential equation when a suitable entropy inequality is enforced.

Jameson, A.↗
NASA NTRS1992

Neural network training by integration of adjoint systems of equations forward in time

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Toomarian, Nikzad↗
NASA NTRS1999

Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Toomarian, Nikzad↗
NASA NTRSDate not supplied

Spacesuit Sizing by Multivariate Simulation: Case Study for Liquid Cooling and Ventilation Garment

A technique was developed to assess the fit of spacesuit garment liquid cooling and ventilation garment (LCVG). A fit scoring scheme was built from the spacesuit sizing requirements and guidelines, and the accommodated proportion of the wearer population was estimated from statistically synthesized pseudo population data. The method evaluated different scenarios of LCVG sizing systems including 1) baseline 7-size system, 2) 7-sizes with target body dimensions iteratively adjusted for maximum fit, and 3) 9-sizes with iterative adjustments. Overall, the baseline sizing system showed 81% accommodation rate, while the hypothetical new systems in-tegrating iterative adjustments for 7- and 9-sizes predictively indicated that accommodation could improve up to 92 and 97%. The proposed method provided a structured metric to quantify fit performance of a garment sizing system, which can be further applied to different spacesuit component, PPE and garment designs.

Han Kim↗
NASA NTRS1979

Improvements in surface singularity analysis and design methods

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Bristow, D. R.↗
NASA NTRS1977

Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics

Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.

Martin, E. D.↗
NASA NTRS1982

Calculation of vortex flows on complex configurations

The calculation of aerodynamic characteristics of complex configurations having strongly coupled vortex flows is a non-linear problem requiring iterative solution techniques. This paper discusses the use of a low-order panel method as a means of obtaining practical solutions to such problems. The panel method is based on piecewise constant source and doublet quadrilateral panels and uses the internal Dirichlet boundary condition of zero perturbation potential. The problems of predicting vortex/surface interaction and vortex separation are discussed. Some example calculations are included but further test cases have yet to be carried out, in particular for comparisons with experimental data. The problem of convergence on the iterative calculation for the shape of the free vortex sheet is addressed and a preprocessor routine, based on an unsteady, two-dimensional version of the panel method, is put forward as a cost-effective way of generating an initial vortex structure for use as a starting solution for general configurations.

Maskew, B.↗
DOE OSTI2022

Online data-enabled predictive control

We develop an online data-enabled predictive (ODeePC) control method for optimal control of unknown systems, building on the recently proposed DeePC (Coulson et al., 2019). Our proposed ODeePC method leverages a primal-dual algorithm with real-time measurement feedback to iteratively compute the corresponding real-time optimal control policy as system conditions change. The proposed ODeePC conceptual-wise resembles standard adaptive system identification and model predictive control (MPC), but it provides a new alternative for the standard methods. ODeePC is enabled by computationally efficient methods that exploit the special structure of the Hankel matrices in the context of DeePC with Fast Fourier Transform (FFT) and primal-dual algorithm We provide theoretical guarantees regarding the asymptotic behavior of ODeePC, and we demonstrate its performance through numerical examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1969

Determination of the temperature profile in an atmosphere from its outgoing radiation

A highly convergent relaxation method for the inversion of the full radiative transfer equation was developed. The results of the iterative solution indicate that convergence can be achieved over a wide range of initial guesses, enabling the temperature profile of a relatively unknown atmosphere to be unambiguously determined. The method is illustrated by examples for the outgoing radiance in the earth's atmosphere for the region of the 4.3 microns CO2 band, but can be similarly applied in other frequency ranges.

Chahine, M. T.↗
NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗
DOE OSTI2024

Non-disruptive error field measurement in DIII-D low safety factor plasmas and projection to ITER

Previous experiments in DIII-D (Paz-Soldan et al 2022 Nucl. Fusion 62 126007) introduced a method to identify intrinsic error fields (EFs) in tokamaks with minimal disruption risk by promptly healing driven magnetic islands during the conventional 'compass scan'. This paper presents recent experimental and numerical advancements in extending this approach to low q 95 plasmas, and projects its applicability to ITER. Non-disruptive EF measurement is achieved at q 95 = 4.5 and 3.9 without any initial EF correction (EFC) by reducing the time between the occurrence of the locked mode (LM) and control action to 10 ms and increasing the density 50%–100%. However, 50% correction of the intrinsic EF is required to achieve island healing at q 95 = 3.2 with 10 ms delay for the control action. Nonlinear two-fluid modeling with the TM1 code reproduces the DIII-D experimental observations, indicating that promptly turning off the 3D coil current reduces both magnetic island width and electromagnetic force, while raising the density increases plasma viscosity, facilitating magnetic island healing. The simulations show that for scenarios with q 95 = 3.2, lowering the control action time to 5 ms will lead to island healing without EFC. TM1 simulations are extended to future ITER scenarios with 5 MA and 7.5 MA plasma currents, predicting the dependence of required density rise on action time and EF amplitude. These simulations indicate that, benefiting from the much longer resistive time, island healing can be successfully achieved in ITER when taking control action 100–500 ms after a LM occurrence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Diffusion Synthetic Acceleration for Heterogeneous Domains, Compatible with Voids

A standard approach to solving the S N transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using O(1) AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

Direct method for solution of three-dimensional unsteady incompressible Navier-Stokes equations

A three-dimensional, unsteady analysis for the velocity-vorticity formulation of the Navier-Stokes (NS) equations is described. This formulation highlights the natural separation of the spin dynamics of a fluid particle from its translational kinematics. This separation is exploited to produce a single pass direct inversion of the full unsteady NS operator without the need to iterate either the future wall vorticity or the nonlinear vorticity convection terms. The method has uniform second-order accuracy in time and space. As an example, it is applied to the problem of the three-dimensional flow within a shear-driven cubical box. Results are obtained for Re = 100, 400, and 1000 using a preliminary (25, 25, 25) mesh.

Osswald, G. A.↗
DOE OSTI2022

Fast nonlinear iterative solver for an implicit, energy-conserving, asymptotic-preserving charged-particle orbit integrator

Here recently, an asymptotic-preserving (AP) particle orbit integrator has been proposed with remarkable properties including exact energy conservation, the ability to capture of all first-order drifts (including the ∇B-drift), the ability to capture trapped-passing boundaries with parallel velocity extremely close to the critical velocity, and the ability to transition from strongly to weakly magnetized spatial regions. The new AP orbit integrator is implicit, employing a Crank-Nicolson (CN) temporal discretization to ensure exact energy conservation. This, in turn, requires a local nonlinear iteration involving particle velocities and positions, and the local electromagnetic fields, to obtain the new-time solution. Ref. [1] did not attempt to provide an efficient solver for this system, and employed a brute-force GMRES-driven Jacobian-free Newton-Krylov (JFNK) solver to invert the particle orbit equations at every timestep for expediency. While JFNK is robust and reliable, it is also expensive and very intrusive for practical implementations of the method (it requires having the JFNK machinery available and solving a 6 x 6 Jacobian system iteratively once per iteration per particle).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test.

He, Yuning↗
DOE OSTI2020

Efficient 3-D velocity model building using joint inline and crossline plane-wave wave-equation migration velocity analyses

SUMMARY Wave-equation migration velocity analysis (WEMVA) is an image-domain inversion method for velocity model building. Automatic plane-wave WEMVA (PWEMVA) calculates the moveouts of plane-wave common-image gathers (CIGs) by searching a best-fitting parabola with semblance analysis and backprojects residual CIG moveouts into wavefield wave paths with a reflection tomographic kernel. However, 3-D PWEMVA is very computationally expensive because 3-D reflection tomographic inversion requires at least five 3-D reverse-time migrations per iteration and stores two types of source wavefields at model boundaries. We develop a joint inline and crossline PWEMVA method for efficient 3-D velocity model building. We alternatively implement the inline and crossline PWEMVAs with a constraint for each other, in which we iteratively construct the 3-D velocity model update through 1-D spline interpolation of 2-D gradients. The inline and crossline joint inversion is practical since PWEMVA only inverts for low-wavenumber velocity perturbations along wave paths, and the method can take less than 1 per cent of the computational cost of full 3-D PWEMVA. To construct unaliased plane waves for our joint inline and crossline PWEMVA, we develop a 3-D data interpolation method in the frequency–wavenumber (FK) domain to recover regularly and randomly missing traces. The method minimizes the misfit on sufficiently localized data subsets with iterative optimal step lengths and a gradient preconditioner that iteratively selects dominant dips along different azimuths. In numerical experiments, we use a 3-D synthetic seismic data set and a land 3-D field seismic data set acquired at the Farnsworth CO2-EOR (enhanced oil recovery) field to demonstrate the efficacy of our velocity model building and data interpolation methods.

Liu, Xuejian↗
NASA NTRS1988

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗
NASA NTRS1990

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗