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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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

Domain-based method↗
DOE OSTI2024

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are responsive materials that can undergo large reversible deformations upon exposure to external stimuli, such as electrical and thermal fields. Controlling the alignment of their liquid crystals mesogens to achieve desired shape changes unlocks a new design paradigm that is unavailable when using traditional materials. While experimental measurements can provide valuable insights into their behavior, computational analysis is essential to exploit their full potential. Accurate simulation is not, however, the end goal; rather, it is the means to achieve their optimal design. Such design optimization problems are best solved with algorithms that require gradients, i.e., sensitivities, of the cost and constraint functions with respect to the design parameters, to efficiently traverse the design space. In this work, a nonlinear LCE model and adjoint sensitivity analysis are implemented in a scalable and flexible finite element-based open source framework and integrated into a gradient-based design optimization tool. To display the versatility of the computational framework, LCE design problems that optimize both the material, i.e., liquid crystal orientation, and structural shape to reach a target actuated shapes or maximize energy absorption are solved. Multiple parameterizations, customized to address fabrication limitations, are investigated in both 2D and 3D. The case studies are followed by a discussion on the simulation and design optimization hurdles, as well as potential avenues for improving the robustness of similar computational frameworks for applications of interest.

42 ENGINEERING↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
DOE OSTI2021

A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling

Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn 85 opacity set. The implicit systems arise from the discretization of a nonrelativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems — a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixedpoint iteration and Newton’s method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Here, numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Parallel-in-Time Solution of Hyperbolic PDE Systems via Characteristic-Variable Block Preconditioning

We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Development of Modified Perturbation Solutions to the One-Phase Stefan Problems With a Convective Boundary

The classical Stefan problem is used to track the moving solid-liquid interface during the freezing process. Perturbation theory has often been applied to find an approximate analytical solution due to the nonlinearity of the moving interface. However, the Stefan number (i.e., the sensible over latent heat) must be small and usually less than 0.01 to assume the perturbation expansion, which in turn limits the thermal engineering applications. In this study, a modified perturbation solution is developed by adding a correction term after the leading-order solution to be valid for a much wider range of Stefan numbers (i.e., 0.01 less than or equal to Ste less than or equal to 1). Specifically, a one-phase Stefan problem is first formulated subjected to a convective boundary in the Cartesian, cylindrical, and spherical coordinate systems for inward solidification. The leading-order solution is calculated based on the regular perturbation theory, while the correction term is obtained using the Monte-Carlo method and a multi-variant regression. Results show that the correction term has a linear relationship with the Stefan number and is not significantly influenced by the Biot number. The proposed modified perturbation solution can accurately and rapidly predict the nonlinear moving interface motion for the freezing process.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A remapping scheme for history-dependent material state variables

Here, we present an interpolation scheme for use with material models involving history-dependent state variables. The interpolation scheme is based on the solution of a constrained optimization problem, to identify the smoothest monotone curve which produces an admissible solution. Unlike classical schemes used for transport equations, the proposed methodology accounts for the interdependence of the history variables and produces admissible interpolations of the material's state variables. After introducing a general solution scheme for the problem, a simplified and more computationally efficient method is derived. Finally, as a validation problem for the proposed methods, we consider the advection of internal state variables belonging to material models with highly nonlinear yield surfaces.

42 ENGINEERING↗
DOE OSTI2021

Implicit Multirate GARK Methods

This article considers multirate generalized-structure additively partitioned Runge–Kutta methods for solving stiff systems of ordinary differential equations with multiple time scales. These methods treat different partitions of the system with different timesteps for a more targeted and efficient solution compared to monolithic single rate approaches. With implicit methods used across all partitions, methods must find a balance between stability and the cost of solving nonlinear equations for the stages. In order to characterize this important trade-off, we explore multirate coupling strategies, problems for assessing linear stability, and techniques to efficiently implement Newton iterations for stage equations. Unlike much of the existing multirate stability analysis which is limited in scope to particular methods, we present general statements on stability and describe fundamental limitations for certain types of multirate schemes. New implicit multirate methods up to fourth order are derived, and their accuracy and efficiency properties are verified with numerical tests.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Thermomechanics coupling to Monte Carlo particle transport on unstructured mesh geometries using Cardinal

Geometry deformation due to thermal expansion influences neutron transport in many systems. Studying this phenomenon involves coupling models for neutronics, thermal hydraulics, and solid mechanics. To enable high fidelity modeling of these coupled physics, new capabilities were introduced in Cardinal, coupling OpenMC Monte Carlo particle transport models with MOOSE thermomechanical physics on unstructured moving-mesh geometries. In this work, we present a fully open-source capability leveraging on-the-fly mesh skinning to automatically regenerate OpenMC geometry, which allows multiphysics feedback from temperature, density, and geometry changes. The new capability is verified using an analytic benchmark slab problem, which couples S 2 neutron transport with thermal conduction, convective boundary conditions, Doppler-broadened cross sections, and nonlinear thermal expansion effects along the heated slab. Cardinal reproduces the analytic solutions for the neutron flux, heating, k eff , and temperature with demonstrated convergence in various error terms including mesh resolution and cross section temperature library spacing. For the nominal benchmark conditions and with a fine mesh, maximum relative errors for neutron flux, temperature, and heating are lower than 1%, while errors in integral quantities such as k eff and slab length are within 1 pcm and 48 µm, respectively. This work (i) presents a new numerical approach to thermomechanics coupling with OpenMC models, (ii) is the first (to our knowledge) to utilize a mechanical partial differential equation (PDE) solution to solve the (Griesheimer and Kooreman, 2022) analytic benchmark, and (iii) develops this verified capability within an open-source package.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Mathematical Programming Models for Shale Oil & Gas Development: A Review and Perspective

Here, in this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel Solver Framework for Mixed-Integer PDE-Constrained Optimization

ROL-PEBBL is a C++, MPI-based parallel code for mixed-integer PDE-constrained optimization (MIPDECO). In these problems we wish to optimize (control, design, etc.) physical systems, which must obey the laws of physics, when some of the decision variables must take integer values. ROL-PEBBL combines a code to efficiently search over integer choices (PEBBL = Parallel Enumeration Branch-and-Bound Library) and a code for efficient nonlinear optimization, including PDE-constrained optimization (ROL = Rapid Optimization Library). In this report, we summarize the design of ROL-PEBBL and initial applications/results. For an artificial source-inversion problem, finding sources of pollution on a grid from sparse samples, ROL-PEBBLs solution for the nest grid gave the best optimization guarantee for any general solver that gives both a solution and a quality guarantee.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗
DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗