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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 91 records · Page 5

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

In this work, we propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

97 MATHEMATICS AND COMPUTING↗

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evaluation of Maximum Allowable Working Pressure and Svensson Burst Pressure Recommended in API 579-1 2021 Edition

Abstract API 579-1/ASME FFS-1 2021 Edition provides the minimum wall thickness, the maximum allowable working pressure (MAWP), and the membrane stress equations for thin and thick-walled cylindrical shells subject to internal pressure in Section 2C.3.3.1 of Appendix 2C – Thickness, MAWP, and Stress Equations for an FFS Assessment. The minimum wall thickness and MAWP are determined using the hoop stress and the Tresca yield criterion. Section 2C.7 – Estimation of Burst Pressure newly added the Svensson method for calculating burst pressure of cylindrical shells under internal pressure, where the plastic yielding is characterized by the von Mises yield criterion. For thin-walled cylinders, the von Mises flow solution of burst pressure in Equation (2C.179) was recommended. For thick-walled cylinders, an implicit burst pressure solution in an integral equation (2C.176) was recommended. But this integral equation is inconvenient to use in practice. It is well known that the classic plasticity theory includes the Tresca and von Mises yield criteria, with the Tresca criterion predicting a lower bound solution and the von Mises criteria predicting an upper bound solution. In addition, the present author developed an average shear stress yield criterion that can determine more accurate limit and burst pressures for thin and thick-walled cylinders. This work uses these three yield criteria to evaluate the minimum required wall thickness, MAWP and Svensson burst pressure recommended in the API 579 code.

burst pressure↗

Demonstration of a new unstructured mesh IMC x-ray transport capability in LAP codes

In this document, the Advanced Simulation and Computing (ASC) Transport Project’s Jayenne team presents evidence that the Los Alamos National Laboratory (LANL) Level 2 milestone statement, Demonstrate a new unstructured mesh IMC x-ray transport capability in LAP codes, due Q4 FY20, has been satisfied with the release and integration of the Jayenne team’s Implicit Monte Carlo (IMC) solver libraries into the lumos multiphysics solver. The Jayenne project’s software includes the algorithms and features prescribed by the milestone description. The lumos software is maintained by the Lagrangian Applications Project (LAP) along with the hydrodynamics code flag and operates under the same ASC program as Jayenne. A set of demonstration problems has been specified, executed, and analyzed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Highlights for DOE ASCR Applied Math Office [Slides]

An efficient Picard-based solver is proposed for a novel energy conserving particle integrator preserving all first-order guiding center drifts and correct gyroradius for large time steps in arbitrary (non-uniform) magnetic fields. This research enables the efficient deployment of the novel asymptotic preserving (AP) particle orbit integrator into modern energy-conserving, implicit particle-in-cell codes, delivering a truly multiscale simulation capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Compositional Methods for Schrödinger's Equation with Application to Optimal Control

The evolution of the state of a quantum computer is governed by Schrödinger's equation. We introduce compositional methods, a way to increase the order of symmetric methods by replacing one timestep by multiple timesteps. We perform several numerical experiments, including a simulation of a two qubit CNOT gate, using compositional variants of Störmer-Verlet and the implicit midpoint rule. We observe that the compositional methods demonstrate greater computational efficiency than the base methods when the desired error tolerance is less than ~ 10 -4 to 10 -5 . We discuss the trade-offs of using each compositional method, as well as differences between using Störmer-Verlet or the implicit midpoint rule as the base integrator of the compositional methods.

97 MATHEMATICS AND COMPUTING↗

Evaluation of Maximum Allowable Working Pressure and Svensson Burst Pressure Recommended in API 579-1 2021 Edition

ABSTRACT API 579-1/ASME FFS-1 2021 Edition provides the minimum wall thickness, the maximum allowable working pressure (MAWP), and the membrane stress equations for thin and thick-walled cylindrical shells subject to internal pressure in Section 2C.3.3.1 of Appendix 2C – Thickness, MAWP, and Stress Equations for an FFS Assessment. The minimum wall thickness and MAWP are determined using the hoop stress and the Tresca yield criterion. Section 2C.7 – Estimation of Burst Pressure newly added the Svensson method for calculating burst pressure of cylindrical shells under internal pressure, where the plastic yielding is characterized by the von Mises yield criterion. For thin-walled cylinders, the von Mises flow solution of burst pressure in Equation (2C.179) was recommended. For thick-walled cylinders, an implicit burst pressure solution in an integral equation (2C.176) was recommended. But this integral equation is inconvenient to use in practice. It is well known that the classic plasticity theory includes the Tresca and von Mises yield criteria, with the Tresca criterion predicting a lower bound solution and the von Mises criteria predicting an upper bound solution. In addition, the present author developed an average shear stress yield criterion that can determine more accurate limit and burst pressures for thin and thick-walled cylinders. This work uses these three yield criteria to evaluate the minimum required wall thickness, MAWP and Svensson burst pressure recommended in the API 579 code.

burst pressure↗

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A novel implicit hybrid machine learning model and its application for reinforcement learning

A novel methodology to develop implicit hybrid models is presented. PyTorch is used to integrate physics-based equations with machine learning models. Automatic differentiation of the hybrid model is leveraged to solve the implicit equations. Iterative solving enables gradient based updates to the machine learning model. The novel methodology is compared to an explicit hybrid approach on a continuously stirred tank reactor (CSTR). The novel method results in a lower modelling error. Both hybrid models effectively train with noisy data. To test the implicit hybrid model, it is employed as a reinforcement learning (RL) training model. The RL algorithm trained on the hybrid model outperforms real time optimization of the CSTR and performs nearly as well as RL trained directly on the CSTR and a traditional gradient based approach. Training RL directly on the CSTR requires over 60,000 system interactions compared to 6000 historical data points for hybrid model development.

42 ENGINEERING↗

Electromagnetic Transient Simulation of Photovoltaic Inverter Using Implicit-Explicit Solver

This paper introduces the implementation of electromagnetic transient (EMT) simulations of a photovoltaic (PV) inverter module using the Implicit-Explicit (ImEx) solver in the Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS). This study demonstrates the effectiveness of the ImEx solver in overcoming the challenges inherent in simulating the complex dynamics of PV inverter modules. Furthermore, using SUNDIALS’ ImEx solver module ARKODE for EMT simulation automates key aspects of the process, such as numerical integration, providing substantial benefits including enhanced consistency, faster implementation, reduced human error, and the capability to handle the complexities of advanced numerical integration. By conducting comparative simulations with an implicit method used in commercial software, the research showcases the ImEx solver’s capability in achieving high accuracy and reliability. Results indicate that leveraging the ImEx approach significantly enhances modeling fidelity and reduces simulation setup times, offering a promising tool for the EMT analysis of PV inverter systems in power electronics-dominated power grids.

Choi, Jongchan [ORNL] (ORCID:000000025952455X)↗

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗

A high-order finite difference method for moving immersed domain boundaries and material interfaces

Here, we present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up to sixth order accuracy for diffusion terms and third order accuracy for advection terms. The temporal discretization relies on a novel strategy for maintaining high-order temporal accuracy in problems with moving boundaries that minimizes implementation complexity and allows arbitrary explicit or diagonally-implicit Runge-Kutta schemes. The approach is broadly compatible with popular PDE-specialized Runge-Kutta time integrators, including low-storage, strong stability preserving, and diagonally implicit schemes. Through numerical experiments we demonstrate that the full discretization maintains high-order spatial and temporal accuracy in the presence of complex 3D geometries and for a range of boundary conditions, including Dirichlet, Neumann, and flux conditions with large jumps in coefficients.

97 MATHEMATICS AND COMPUTING↗

Static actuator-sharing algorithm for concurrent control of multiple plasma properties

Simultaneous regulation of multiple properties in next-generation tokamaks like ITER and fusion pilot plant may require the integration of different plasma control algorithms. Such integration requires the conversion of individual controller commands into physical actuator requests while accounting for the coupling between different plasma properties. This work proposes a tokamak and scenario-agnostic actuator-sharing algorithm (ASA) to perform the above-mentioned command-request conversion and, hence, integrate multiple plasma controllers. The proposed algorithm implicitly solves a quadratic programming (QP) problem formulated to account for the saturation limits and the relation between the controller commands and physical actuator requests. Since the constraints arising in the QP program are linear, the proposed ASA is highly computationally efficient and can be implemented in the tokamak plasma control system in real time. Furthermore, the proposed algorithm is designed to handle real-time changes in the control objectives and actuators’ availability. Nonlinear simulations carried out using the Control Oriented Transport SIMulator illustrate the effectiveness of the proposed algorithm in achieving multiple control objectives simultaneously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Converging towards atomic and nuclear pressures (Final Report)

his report details the development of transformational tools and techniques, allowing the accurate characterization of matter at the most extreme conditions yet studied in the high energy density (HED) domain. Before this work, most experiments quantitatively mapping the nature of matter in the HED realm were performed using planar geometry, which allows for the isolation and measurement of variables in a single thermodynamic state. Such measurements include equation of state variables, optical conductivity, heat transport and more. However, due to a variety of plasma processes, such experiments are limited to below ~10 TPa (100 Mbar) pressures. To achieve higher pressures, convergent experiments are needed. Historically, convergent experiments have not been used for benchmark data because they are integral measurements. That is each part of a convergent target undergoes a time dependent wide range of states, making it difficult to accurately isolate any particular quantity for a given thermodynamic state. This effort developed innovative convergent HED platforms and techniques enabling the exploration of matter from atomic to nuclear scale pressures. This effort also performed pioneering experiments that yielded the first rigorous benchmark data at these extreme conditions. This funding award began with the overarching goal to understand the behavior of matter at extreme (atomic-to-nuclear scale) pressures. The motivation for these goals lie in the fact that every time scientists explore matter beyond the threshold of an atomic unit, there is a fundamental shift in science. The atomic unit for energy, mass, charge, length, and time have each been explored, and each time such a threshold was crossed, a new sequence of discoveries was made resulting in significant awards such as the Nobel Prize. The only unexplored atomic unit is pressure, and this effort set the course for exploring matter at and beyond such pressures. That most of the recently discovered extrasolar planets and stars, as well as matter in the late implosion stages of inertial fusion targets, have deep internal pressures at and beyond atomic pressures amplifies the importance of this effort. Much of the initial work in developing techniques to create these atomic-to-nuclear pressures already existed within the HED community, predominantly at large scale laser facilities such as the National Ignition Facility (NIF) and the Omega60 laser the University of Rochester and although these experiments were routinely performed the ability to extract information about the underlying physical states and processes remained elusive due to the complexity of the experiments, extreme scales in both time and space, and the integrated nature of all the measurements. This work built a rigorous framework so such measurements can routinely be made. This was done in part through the introduction of Bayesian inference techniques into the field of HED science. These techniques allow for the self-consistent extraction of the relevant variables and their explicit and implicit correlations, so as to make use of integrated experimental data to constrain physical models and provide accurate uncertainty bounds for the data. The techniques developed here are fully transparent and proved immediately useful providing quantitative rigorous benchmarks for physical states and processes at some of the most extreme conditions yet explored on Earth. This funding is directly or partly responsible for 7 publications in major peer-reviewed scientific journals, a doctoral thesis, 3 invited talks at major conferences, and the training of a post-doc, 2 graduate students, and 1 undergraduate student. Beyond the effort supported by this award launched the introduction of Bayesian inference into the HED physics community and helped push the usage if modern data-science techniques within the physics community at large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗