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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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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Verification of Viscous Goal-Based Anisotropic Mesh Adaptation

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics. A key ingredient for the broader acceptance of unstructured mesh adaptation is the verification of these implementations. Anisotropic metric construction methods are evaluated with analytically defined primal fields and the corresponding entropy variables as adjoint fields. This allows the comparison of different metric formulations and different implementations of the same formulation without the complications of a flow and adjoint solution method. The convergence of the output associated with the entropy variable adjoint is studied for mesh adaptation to these fields and a manufactured solution. Mesh adapted drag output is studied for two simple wings in compressible laminar flow to show fine-mesh convergence of multiple metric construction methods to less than a single drag count. The documentation of these verification exercises helps to prepare these goal-based methods for routine use in more complex simulations for production workflows.

mesh adaptation↗
NASA NTRS1995

Improved Adjoint-Operator Learning For A Neural Network

Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).

Toomarian, Nikzad↗
NASA NTRS1991

Active control of panel vibrations induced by boundary-layer flow

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

Chow, Pao-Liu↗
NASA NTRS1993

Boundary layer receptivity and control

Receptivity processes initiate natural instabilities in a boundary layer. The instabilities grow and eventually break down to turbulence. Consequently, receptivity questions are a critical element of the analysis of the transition process. Success in modeling the physics of receptivity processes thus has a direct bearing on technological issues of drag reduction. The means by which transitional flows can be controlled is also a major concern: questions of control are tied inevitably to those of receptivity. Adjoint systems provide a highly effective mathematical method for approaching many of the questions associated with both receptivity and control. The long term objective is to develop adjoint methods to handle increasingly complex receptivity questions, and to find systematic procedures for deducing effective control strategies. The most elementary receptivity problem is that in which a parallel boundary layer is forced by time-harmonic sources of various types. The characteristics of the response to such forcing form the building blocks for more complex receptivity mechanisms. The first objective of this year's research effort was to investigate how a parallel Blasius boundary layer responds to general direct forcing. Acoustic disturbances in the freestream can be scattered by flow non-uniformities to produce Tollmien-Schlichting waves. For example, scattering by surface roughness is known to provide an efficient receptivity path. The present effort is directed towards finding a solution by a simple adjoint analysis, because adjoint methods can be extended to more complex problems. In practice, flows are non-parallel and often three-dimensional. Compressibility may also be significant in some cases. Recent developments in the use of Parabolized Stability Equations (PSE) offer a promising possibility. By formulating and solving a set of adjoint parabolized equations, a method for mapping the efficiency with which external forcing excites the three-dimensional motions of a non-parallel boundary layer was developed. The method makes use of the same computationally efficient formulation that makes the PSE currently so appealing. In the area of flow control, adjoint systems offer a powerful insight into the effect of control forces. One of the simplest control strategies for boundary layers involves the application of localized mean wall suction.

Hill, D. C.↗
NASA NTRSDate not supplied

Enabling Supersonic Over-Land Flight Using Computational Modeling

NASA's QueSST mission is interested in exploring the potential of commercial, over-land supersonic flight, which has been banned since 1973 due to the noise intensity of the sonic booms that supersonic vehicles create. NASA has partnered with Lockheed Martin to design and construct an experimental aircraft, the X-59, that will shape the sonic boom to achieve a perceived loudness on the ground that is lower than 75dB. In this talk, we present new developments in the Launch Ascent and Vehicle Aerodynamics (LAVA) CFD solver framework which are tailored to the analysis of supersonic vehicles, like the X-59, and sonic boom propagation. Utilizing a high-order space marching method, adjoint-based grid adaptation, and robust database capabilities have enabled significant cost savings over traditional CFD methods for the same level of accuracy in perceived boom loudness. Example cases demonstrating the toolset are presented, along with comparisons to experimental wind tunnel data. These developments will enable LAVA to quickly and accurately provide simulation data to the project during X-59's first and subsequent flights in 2024 and beyond.

CST↗
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 NTRS1986

Design sensitivity analysis using EAL. Part 2: Shape design parameters

A numerical implementation of shape design sensitivity analysis of built-up structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its data base management system. This report is a continuation of a previous report on conventional design parameters. The finite element code used in the implementation presented is the Engineering Analysis Language (EAL), which is based on a hybrid analysis method. It has been shown that shape design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate data base. The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to derive shape design sensitivity information of structural performances. A domain method of shape design sensitivity analysis and a design component method are used. Displacement and stress functionals are considered as performance criteria.

Dopker, B.↗
NASA NTRS1985

Shape design sensitivity analysis using domain information

A numerical method for obtaining accurate shape design sensitivity information for built-up structures is developed and demonstrated through analysis of examples. The basic character of the finite element method, which gives more accurate domain information than boundary information, is utilized for shape design sensitivity improvement. A domain approach for shape design sensitivity analysis of built-up structures is derived using the material derivative idea of structural mechanics and the adjoint variable method of design sensitivity analysis. Velocity elements and B-spline curves are introduced to alleviate difficulties in generating domain velocity fields. The regularity requirements of the design velocity field are studied.

Seong, Hwal-Gyeong↗
NASA NTRS2005

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗
NASA NTRS2006

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗
NASA NTRS1985

Sensitivity derivatives for static test loading boundary conditions

Attention is given to the application of the adjoint variable method under the special combination of displacement and stress boundary conditions which occur when static test conditions are simulated. In the two-step problem-solving method employed, calculation of internal stresses, displacements and total reaction force at the boundary is followed by the calculation of the applied load and the total reaction force due to unit displacements.

Gurdal, Z.↗
NASA NTRS1987

Shape design sensitivity analysis and optimal design of structural systems

The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to relate variations in structural shape to measures of structural performance. A domain method of shape design sensitivity analysis is used to best utilize the basic character of the finite element method that gives accurate information not on the boundary but in the domain. Implementation of shape design sensitivty analysis using finite element computer codes is discussed. Recent numerical results are used to demonstrate the accuracy obtainable using the method. Result of design sensitivity analysis is used to carry out design optimization of a built-up structure.

Choi, Kyung K.↗
NASA NTRS1989

On the accuracy of shape sensitivity derivatives

Six methods for calculating shape sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the finite-element mesh is refined, displacement sensitivity derivatives converge more slowly than the displacement themselves. Five of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer, rather than reduced accuracy.

Haftka, Raphael T.↗
NASA NTRS1991

On the accuracy of shape sensitivity

The calculation of sensitivity of the response of a structure modeled by finite elements to shape variation is known to be subject to numerical difficulties. The accuracy of a given method is typically measured against the yard stick of finite-difference sensitivity calculation. The present paper demonstrates with a simple example that this approach may be flawed because of discretization errors associated with the finite element mesh. Seven methods for calculating sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the mesh is refined, displacement sensitivity derivatives converge more slowly than the displacements. Six of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer rather than reduced accuracy. Additionally, it is observed that small derivatives are particularly prone to accuracy problems.

Haftka, R. T.↗
NASA NTRS1991

Discrete shape sensitivity equations for aerodynamic problems

Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysis methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a preelimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.

Hou, Gene J.-W.↗
NASA NTRS1993

Sensitivity analysis of Lyapunov and Riccati equations with application to controls-structures integrated design

Controls-structure integrated design is a complicated multidisciplinary design optimization problem which involves the state equations pertaining to open-loop eigenvalues and control laws. In order to alleviate the intensity of the computation, this study uses the adjoint variable method to derive sensitivity equations for the eigenvalue, Liapunov, and Riccati equations. These individual sensitivity equations are then combined together to form the multidisciplinary sensitivity equations for the control structure integrated design problems. A set of linear sensitivity equations, proportional in number to the number of performance functions involved in the optimization process, are solved. This proposed approach may provide a great saving in computer resources. The validity of the newly developed sensitivity equations is verified by numerical examples.

Hou, Gene↗