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At least 613 records · Page 34

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DOE OSTI2016

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

A novel partitioning method for block-structured adaptive meshes

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

On the performance of exponential integrators for problems in magnetohydrodynamics

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin–Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H{sub 2} and liquid Al–Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

A stable and accurate partitioned algorithm for conjugate heat transfer

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. Here in this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(10 5 )) moving bodies, utilizing many computational cores (O(10 5 )), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Quantum Fokker-Planck modeling of degenerate electrons

In this work, an implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and electron-electron collision operators are discretized using a discontinuous Galerkin method, and the electron energy distribution is updated by an implicit time integration method. The numerical scheme is designed to satisfy all conservation laws exactly. Numerical tests and comparisons with other modeling approaches are shown to demonstrate the accuracy and conservation properties of the proposed method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

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↗

DOE OSTI2024

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↗

DOE OSTI2017

Flow-induced vibration analysis of a helical coil steam generator experiment using large eddy simulation

This paper describes a numerical study of flow-induced vibration in a helical coil steam generator experiment conducted at Argonne National Laboratory in the 1980s. In the experiment, a half-scale sector model of a steam generator helical coil tube bank was subjected to still and flowing air and water, and the vibrational characteristics were recorded. The research detailed in this document utilizes the multi-physics simulation toolkit SHARP developed at Argonne National Laboratory, in cooperation with Lawrence Livermore National Laboratory, to simulate the experiment. SHARP uses the spectral element code Nek5000 for fluid dynamics analysis and the finite element code DIABLO for structural analysis. The flow around the coil tubes is modeled in Nek5000 by using a large eddy simulation turbulence model. Transient pressure data on the tube surfaces is sampled and transferred to DIABLO for the structural simulation. The structural response is simulated in DIABLO via an implicit time-marching algorithm and a combination of continuum elements and structural shells. Tube vibration data (acceleration and frequency) are sampled and compared with the experimental data. Currently, only one-way coupling is used, which means that pressure loads from the fluid simulation are transferred to the structural simulation but the resulting structural displacements are not fed back to the fluid simulation

CFD↗

DOE OSTI2020

Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

This study proposes an automated calibration procedure for bond parameters in bonded discrete element modelling. By exploring the underlying physical correlations between microscopic parameters of bonds and macroscopic strength parameters of the continuum to be modelled, the microscopic shear strength and tensile strength are identified as independent variables for calibration purpose. Then a physics-informed iterative scheme is proposed to automatically approximate the bond parameters by viewing the micro-macro relation as an implicitly defined mathematical mapping function. As a result of highly non-convex features of this implicit mapping, the adaptive moment estimation (Adam), which is especially suitable for problems with noisy gradients, is adopted as the basic iterative scheme, in conjunction with other numerical techniques to approximately evaluate the partial derivatives involved. The whole procedure offers a simple and effective framework for bond parameter calibration. Finally, a numerical example of SiC ceramic is provided for validation. By compared with some existing calibration methods, the proposed method shows significant advantages in terms of calibration efficiency and accuracy.

42 ENGINEERING↗

DOE OSTI2025

Ten-moment fluid modeling of the Weibel instability

We investigate the one-dimensional non-relativistic Weibel instability through the capture of anisotropic pressure tensor dynamics using an implicit 10-moment fluid model that employs the electromagnetic Darwin approximation. The results obtained from the 10-moment model are compared with an implicit particle-in-cell simulation. The linear growth rates obtained from the numerical simulations are in good agreement with the theoretical fluid and kinetic dispersion relations. The fluid dispersion relations are derived using Maxwell’s equations and the Darwin approximation. We also show that the magnetohydrodynamic approximation can be used to model the Weibel instability if one accounts for an anisotropic pressure tensor and unsteady terms in the generalised Ohm’s law. In addition, we develop a preliminary theory for the saturation magnetic field strength of the Weibel instability, showing good agreement with the numerical results.

Kuldinow, D. A. (ORCID:0000000319730196)↗

DOE OSTI2018

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.

Yang, Xiu↗

DOE OSTI2024

Prediction of Redox Potentials for U, Np, Pu, and Am in Aqueous Solution

The redox properties of the actinides in aqueous solution are important for fuel production/reprocessing and understanding the environmental impact of nuclear waste. The redox potentials for U, Np, Pu, and Am in oxidation states from 0 up to VII (as appropriate) in aqueous solutions have been predicted at the density functional theory level with the B3LYP functional, Stuttgart small core pseudopotential basis sets for the actinides, and explicit (30H 2 O molecules)/implicit treatment of the aqueous solvent using the self-consistent reaction field COSMO and SMD approaches for the implicit solvation. The predictions of the structural parameters of clusters incorporating first and second solvation shells are consistent with the available experimental data., Our results are typically within 0.2 V of the available experimental data using two explicit solvation shells with an implicit solvent model. The use of the PW91 functional substantially improved the prediction of the Pu(VI/V) redox couple. The redox couples for An(VI/IV) and An(V/IV) which involve the addition of protons and removal of the actinyl oxygens led to slightly larger differences from experiment. Here, the An(IV/0) and An(III/0) couples were reliably predicted with our approach. Predictions of the unknown An(II/I) redox potentials were negative, consistent with expectations, and predictions for unknown An(VII/VI), An(III/II), and An(II/0) redox couples improve prior estimates.

Actinides↗

DOE OSTI2024

BEAST DB: Grand-Canonical Database of Electrocatalyst Properties

We present BEAST DB, an open-source database comprised of ab initio electrochemical data computed using grand-canonical density functional theory in implicit solvent at consistent calculation parameters. The database contains over 20,000 surface calculations and covers a broad set of heterogeneous catalyst materials and electrochemical reactions. Calculations were performed at self-consistent fixed potential as well as constant charge to facilitate comparisons to the computational hydrogen electrode. This article presents common use cases of the database to rationalize trends in catalyst activity, screen catalyst material spaces, understand elementary mechanistic steps, analyze the electronic structure, and train machine learning models to predict higher fidelity properties. Users can interact graphically with the database by querying for individual calculations to gain a granular understanding of reaction steps or by querying for an entire reaction pathway on a given material using an interactive reaction pathway tool. BEAST DB will be periodically updated, with planned future updates to include advanced electronic structure data, surface speciation studies, and greater reaction coverage.

database↗

DOE OSTI2019

Affordable Estimation of Solvation Contributions to the Adsorption Energies of Oxygenates on Metal Nanoparticles

Electrocatalysts are mainly characterized by their intrinsic adsorption properties. However, the observed electrocatalytic activity ultimately results from the interplay between such properties and various additional interactions within the electrified solid–liquid interface. One of such phenomena is solvation, which can substantially affect the stability of adsorbates. The incorporation of solvation in computational electrocatalysis models can be fully implicit (inaccurate for H-bonded adsorbates), fully explicit (challenging computation of free energies), or embedded. Here, we show that without any need for explicit or implicit media, a microsolvation approach with just three water molecules captures the contribution of co-adsorbed water to the adsorption energies of *OH and *OOH (two important adsorbates for oxygen reduction) on platinum nanoparticles of various sizes. The approach enables an accurate yet inexpensive explicit modeling of solvent–adsorbate interactions in nanoparticles and the calculation of solvation corrections, estimated as -0.59 ± 0.14 and -0.47 ± 0.13 eV for *OH and *OOH adsorption on Pt, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗