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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Implications for jet noise reduction and turbulence control in general are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Adjoint method and runaway electron avalanche

The adjoint method for the study of runaway electron dynamics in momentum space Liu et al (2016 Phys. Plasmas 23 010702) is rederived using the Green's function method, for both the runaway probability function (RPF) and the expected loss time (ELT). The RPF and ELT obtained using the adjoint method are presented, both with and without the synchrotron radiation reaction force. In conclusion, the adjoint method is then applied to study the runaway electron avalanche. Both the critical electric field and the growth rate for the avalanche are calculated using this fast and novel approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems

We report the fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian–Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge–Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space–time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier–Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

An adjoint method for neoclassical stellarator optimization

Stellarators remain an enticing route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring $O(N)$ flux computations, where $N$ is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ( $O(10^{2})$ ), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Moreover, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Dataset from: "Adjoint methods for quasisymmetry of vacuum fields on a surface"

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared to finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasisymmetry and a rotational transform value on a surface. To measure quasisymmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Adjoint methods for quasi-symmetry of vacuum fields on a surface

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared with finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasi-symmetry and a rotational transform value on a surface. Here to measure quasi-symmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Neural-adjoint method for the inverse design of all-dielectric metasurfaces

All-dielectric metasurfaces exhibit exotic electromagnetic responses, similar to those obtained with metal-based metamaterials. Research in all-dielectric metasurfaces currently uses relatively simple unit-cell designs, but increased geometrical complexity may yield even greater scattering states. Although machine learning has recently been applied to the design of metasurfaces with impressive results, the much more challenging task of finding a geometry that yields a desired spectra remains largely unsolved. We propose and demonstrate a method capable of finding accurate solutions to ill-posed inverse problems, where the conditions of existence and uniqueness are violated. A specific example of finding the metasurface geometry which yields a radiant exitance matching the external quantum efficiency of gallium antimonide is demonstrated. We also show how the neural-adjoint method can intelligently grow the design search space to include designs that increasingly and accurately approximate the desired scattering response. The neural-adjoint method is not restricted to the case demonstrated and may be applied to plasmonics, photonic crystal, and other artificial electromagnetic materials.

42 ENGINEERING↗
DOE OSTI2021

An adjoint method for determining the sensitivity of island size to magnetic field variations

An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method for calculation of the island width is that of Cary & Hanson ( Phys. Fluids B, vol. 3, issue 4, 1991, pp. 1006–1014) (with a minor modification), and requires that the residue of the island centre be small. Therefore, the gradient of the residue is calculated in addition. Both the island width and the gradient calculations are verified using an analytical magnetic field configuration introduced by Reiman & Greenside ( Comput. Phys. Commun. , vol. 43, issue 1, 1986, pp. 157–167). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in a National Compact Stellarator Experiment (NCSX) vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied by Hanson & Cary ( Phys. Fluids , vol. 27, issue 4, 1984, pp. 767–769) to minimize stochasticity by adding perturbations to a pair of helical coils. Although only vacuum magnetic fields and an analytical magnetic field model are considered in this work, the adjoint calculation of the island width gradient could also be applied to a magnetohydrodynamic (MHD) equilibrium if the derivative of the magnetic field, with respect to the equilibrium parameters, is known. Using the island width gradient calculation presented here, more general gradient-based optimization methods can be applied to design stellarators with small magnetic islands. Moreover, the sensitivity of the island size may itself be optimized to ensure that coil tolerances, with respect to island size, are kept as high as possible.

Physics↗
DOE OSTI2026

Simulation of Channel Flow with Square Ribs for Blanket First-Wall Cooling: Geometry-Specific Tuning of k-ω Model Using Adjoint Method

Cooling of the plasma-facing first wall is challenging in the design of blanket components because of the high heat flux (on the order of 𝑀𝑊/𝑚2) from the plasma, especially when a low thermal mass medium like helium is chosen as the coolant. Therefore, heat transfer enhancement in which the convective heat transfer rate is augmented by the addition of turbulence-promoting structures becomes a key initiative for providing sufficient cooling capability with helium. Previously, computational fluid dynamics simulations had been performed on pipe flows with different transverse and longitudinal ribbed geometries at Oak Ridge National Laboratory to compare the enhancement performance among different ribbed geometries. Rib shape morphing had been conducted to obtain an optimized rib profile. In the work presented here, the adjoint method is adopted in the ANSYS Fluent solver for turbulence model augmentation, and the Generalized k-ω (GEKO) turbulence model is employed because of its ability of tuning the turbulence model. The Nusselt number and pressure drop obtained from the channel flow with bottom ribbed wall experiments are used as the targets. Sensitivity analysis provides information as guidance to improve the turbulence model accuracy. The augmented GEKO model is tuned for the studied ribbed channel geometry and flow conditions, providing improved predictive accuracy within this context. Extension to other configurations offers potential but may require additional tuning and validation.

Xu, Tracy [ORNL] (ORCID:0009000193700887)↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An adjoint-based method for optimising MHD equilibria against the infinite- n , ideal ballooning mode

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-n ideal ballooning mode. We present three finite-β (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗