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At least 127 records · Page 7

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids by Using Complex Variables

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

Nielsen, Eric J.↗

Examination of Observation Impacts derived from OSEs and Adjoint Models

With the adjoint of a data assimilation system, the impact of any or all assimilated observations on measures of forecast skill can be estimated accurately and efficiently. The approach allows aggregation of results in terms of individual data types, channels or locations, all computed simultaneously. In this study, adjoint-based estimates of observation impact are compared with results from standard observing system experiments (OSEs) in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) GEOS-5 system. The two approaches are shown to provide unique, but complimentary, information. Used together, they reveal both redundancies and dependencies between observing system impacts as observations are added or removed. Understanding these dependencies poses a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.

Gelaro, Ronald↗

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

remote sensing↗

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗

Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.

Rallabhandi, Sriram K.↗

Top-down Estimate of Dust Emissions Through Integration of MODIS and MISR Aerosol Retrievals With the Geos-chem Adjoint Model

Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOSChem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.

MODIS aerosol retrievals↗

Adjoint-Based Mesh Adaptation for the Sonic Boom Signature Loudness

The mesh adaptation functionality of FUN3D is utilized to obtain a mesh optimized to calculate sonic boom ground signature loudness. During this process, the coupling between the discrete-adjoints of the computational fluid dynamics tool FUN3D and the atmospheric propagation tool sBOOM is exploited to form the error estimate. This new mesh adaptation methodology will allow generation of suitable meshes adapted to reduce the estimated errors in the ground loudness, which is an optimization metric employed in supersonic aircraft design. This new output-based adaptation could allow new insights into meshing for sonic boom analysis and design, and complements existing output-based adaptation techniques such as adaptation to reduce estimated errors in off-body pressure functional. This effort could also have implications for other coupled multidisciplinary adjoint capabilities (e.g., aeroelasticity) as well as inclusion of propagation specific parameters such as prevailing winds or non-standard atmospheric conditions. Results are discussed in the context of existing methods and appropriate conclusions are drawn as to the efficacy and efficiency of the developed capability.

Rallabhandi, Sriram K.↗

Mitigation of Engine Inlet Distortion Through Adjoint-Based Design

The adjoint-based design capability in FUN3D is extended to allow efficient gradient- based optimization and design of concepts with highly integrated aero-propulsive systems. A circumferential distortion calculation, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. This newly implemented distortion calculation can be used not only for design but also to drive the existing mesh adaptation process and reduce the error associated with the fan distortion calculation. The design capability is demonstrated by the shape optimization of an in-house aircraft concept equipped with an aft fuselage propulsor. The optimization objective is the minimization of flow distortion at the aerodynamic interface plane of this aft fuselage propulsor.

Ordaz, Irian↗

Adjoint-Based Design of a Distributed Propulsion Concept with a Power Objective

The adjoint-based design capability in FUN3D is extended to allow efficient gradient-based optimization and design of concepts with highly integrated and distributed aero-propulsive systems. Calculations of propulsive power, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. The design capability is demonstrated by the shape optimization and propulsor sizing of NASA’s PEGASUS aircraft concept. The optimization objective is the minimization of flow power at the aerodynamic interface planes for the wing-mounted propulsors, as well as the tail-cone boundary layer ingestion propulsor, subject to vehicle performance and propulsive constraints.

Ordaz, Irian↗

Toward Adjoint-Based Aeroacoustic Optimization for Propeller and Rotorcraft Applications

The goal of the present project is to build a multidisciplinary, rapid, robust, and accurate computational tool to optimize wing-mounted propeller designs. The full Farassat’s formulation F1Afor aeroacoustic analysis is implemented in the open-source software SU2.This extension enables the prediction of far-field noise generated by moving sources. The formulation is verified, for a stationary and rotating sphere in a wind tunnel and for a tiltrotor in forward flight, by comparing the acoustic predictions ofSU2 with the predictions computed by NASA’s aeroacoustics code ANOPP2. The algorithmic differentiation capability of SU2 provides discretely consistent, adjoint-based sensitivity analysis for this formulation. The adjoint-based sensitivities are verified through comparison with complex-step sensitivities

R Omur Icke↗

Design of a Distributed Propulsion Concept Using an Adjoint-Based Approach and Blade Element Theory to Minimize Power

The adjoint-based design capability in FUN3D is extended to allow efficient gradient-based optimization and design of concepts with highly integrated and distributed aero-propulsive systems. Previous work by the authors demonstrated the derivation and application of design sensitivities of flow power and vehicle forces with respect to design variables associated with actuator disk size, loading, and installation on the aircraft. In this work, calculations of propulsive power, shaft power, and propeller efficiency using blade element-based disk loading, along with sensitivity derivatives needed to perform adjoint-based design, have been implemented. This includes the derivation of additional design sensitivities for actuator disk variables with respect to the radial distributions of blade pitch angle and chord length. The blade element-based loading implementation allows us to tailor the actuator disk loading to provide greater design authority and calculate the torque imparted on the flow for the modeling of swirl effects. The design capability is demonstrated by the optimization of NASA's parallel hybrid electric PEGASUS aircraft concept. The optimization objective is the minimization of shaft power at the aerodynamic interface planes for the wing-mounted and tail-cone boundary layer ingestion propulsors, subject to vehicle performance and propulsive constraints.

Irian Ordaz↗

Linearized Frequency-Domain Gust Analysis and Adjoint-Based Sensitivities

Gust analysis is added to a linearized frequency-domain method in FUN3D, a NASA computational fluid dynamics solver. The method linearizes about a nonlinear static equilibrium condition and is therefore appropriate for problems with small perturbations such as transonic stochastic gust analysis. In addition to the gust analysis, adjoint-based sensitivities of stochastic gust constraints are implemented for multidisciplinary design optimization. The linearized frequency-domain gust model and adjoint-based sensitivities are described and verified. The method is applied to an optimization for mass minimization of the AGARD 445.6 wing subject to a stochastic gust constraint limiting the displacement of the wing tip.

Aeroelasticity↗

A direct-adjoint approach for material point model calibration with application to plasticity

Here, this paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton–Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

36 MATERIALS SCIENCE↗

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗

Adjoint-optimized nanoscale light extractor for nitrogen-vacancy centers in diamond

Abstract We designed a nanoscale light extractor (NLE) for the efficient outcoupling and beaming of broadband light emitted by shallow, negatively charged nitrogen-vacancy (NV) centers in bulk diamond. The NLE consists of a patterned silicon layer on diamond and requires no etching of the diamond surface. Our design process is based on adjoint optimization using broadband time-domain simulations and yields structures that are inherently robust to positioning and fabrication errors. Our NLE functions like a transmission antenna for the NV center, enhancing the optical power extracted from an NV center positioned 10 nm below the diamond surface by a factor of more than 35, and beaming the light into a ±30° cone in the far field. This approach to light extraction can be readily adapted to other solid-state color centers.

42 ENGINEERING↗