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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties

In this article we present a class of high order unconditionally strong stability preserving (SSP) implicit two-derivative Runge--Kutta schemes and SSP implicit-explicit (IMEX) multi-derivative Runge--Kutta schemes where the time-step restriction is independent of the stiff term. The unconditional SSP property for a method of order $p>2$ is unique among SSP methods and depends on a backward-in-time assumption on the derivative of the operator. We show that this backward derivative condition is satisfied in many relevant cases where SSP IMEX schemes are desired. We devise unconditionally SSP implicit Runge--Kutta schemes of order up to $p=4$ and IMEX Runge--Kutta schemes of order up to $p=3$. For the multiderivative IMEX schemes, we also derive and present the order conditions, which have not appeared previously. The unconditional SSP condition ensures that these methods are positivity preserving, and we present sufficient conditions under which such methods are also asymptotic preserving when applied to a range of problems, including a hyperbolic relaxation system, the Broadwell model, and the Bhatnagar--Gross--Krook kinetic equation. We present numerical results to support the theoretical results on a variety of problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. As a result, both quantities compare favorably with experiments.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A physics-based ensemble machine-learning approach to identifying a relationship between lightning indices and binary lightning hazard

To convert lightning indices generated by numerical weather prediction experiments into binary lightning hazard, a machine-learning tool was developed. This tool, consisting of parallel multilayer perceptron classifiers, was trained on an ensemble of planetary boundary layer schemes and microphysics parameterizations that generated four different lightning indices over 1 week. In a subsequent week, the multi-physics ensemble was applied and the machine-learning tool was used to evaluate the accuracy. Unintuitively, the machine-learning tool performed better on the testing dataset than the training dataset. Much of the error may be attributed to mischaracterizing the convection. The combination of the machine learning model and simulations could not differentiate between cloud-to-cloud lightning and cloud-to-ground lightning, despite being trained on cloud-to-ground lightning. It was found that the simulation most representative of the local operational model was the most accurate simulation tested.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

STORM: Scrape-off layer turbulence in tokamak fusion reactors

The scrape-off layer of a tokamak fusion reactor carries the plasma exhaust from the hot core plasma to the material surfaces of the reactor vessel. The heat loads imposed by the exhaust are a critical limit on the performance of fusion power plants. Turbulent transport of the plasma regulates the width of the scrape-off layer plasma and must be modelled to understand the intensity of these heat loads. STORM is a plasma turbulence code capable of simulating three dimensional turbulence across the full scrape-off layer of a tokamak fusion reactor, using a drift reduced, collisional fluid model. STORM uses mostly finite difference schemes, with a staggered grid in the direction parallel to the magnetic field. We describe the model, geometry and initialisation options used by STORM, as well as the numerical methods, which are implemented using the BOUT++ plasma simulation framework. BOUT++ has been enhanced alongside the development of STORM, providing better support for staggered grid methods. We summarise these enhancements, including a detailed explanation of the parallel derivative methods, which underwent a major update for version 4 of BOUT++.

BOUT++↗
DOE OSTI2020

An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

In this paper, we consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗
DOE OSTI2021

Velocity-Space Hybridization of Direct Simulation Monte Carlo and a Quasi-Particle Boltzmann Solver

This paper presents a new method for modeling rarefied gas flows based on hybridization of direct simulation Monte Carlo (DSMC) and discrete velocity method (DVM)-based quasi-particle representations of the velocity distribution function. It is aimed at improving the resolution of the tails of the distribution function (compared with DSMC) and computational efficiency (compared with DVM). Details of the method, such as the collision algorithm and the particle merging scheme, are discussed. The hybrid approach is applied to the study of noise in a Maxwellian distribution, computation of electron-impact ionization rate coefficient, as well as numerical simulation of a supersonic Couette flow. The hybrid-based solver is compared with pure DSMC and DVM approaches in terms of accuracy, computational speed, and memory use. It is shown that such a hybrid approach can provide a lower computational cost than a pure DVM approach, while being able to retain accuracy in modeling high-velocity tails of the distribution function. For problems where trace species have a significant impact on the flow physics, the proposed method is shown to be capable of providing better computational efficiency and accuracy compared with standard fixed-weight DSMC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Towards modelling AR Sco: generalized particle dynamics and strong radiation-reaction regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realized the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time-step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform E- and B-fields and a static dipole B-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time-steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand–Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytical Aristotelian Electrodynamics expectations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Noninteracting electrons in a prototypical one-dimensional sinusoidal potential

A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied, where the argument of the cosine potential energy, periodic with the lattice, contains the first reciprocal lattice vector G 1 =2π/a, where a is the lattice constant. The time-independent Schrödinger equation can be written in reduced variables as a Mathieu equation for which numerically exact solutions for the band structure and wave functions are obtained. The band structure has band gaps that increase with increasing amplitude q of the cosine potential. In the extended-zone scheme, the energy gaps decrease with increasing index n of the Brillouin-zone boundary ka=nπ, where k is the crystal momentum of the electron. The wave functions of the band electron are derived for various combinations of k and q as complex combinations of the real Mathieu functions with even and odd parity, and the normalization factor is discussed. The wave functions at the bottoms and tops of the bands are found to be real or imaginary, respectively, corresponding to standing waves at these energies. Irrespective of the wave vector k within the first Brillouin zone, the electron probability density is found to be periodic with the lattice. The Fourier components of the wave functions are derived versus q, which reveal multiple reciprocal-lattice-vector components with variable amplitudes in the wave functions unless q = 0. The magnitudes of the Fourier components are found to decrease exponentially as a power of n for n~3 to 45 for ka = π/2 and q = 2, and a precise fit is obtained to the data. The probability densities and probability currents obtained from the wave functions are also discussed. The probability currents are found to be zero for crystal momenta at the tops and bottoms of the energy bands, because the wave functions for these crystal momenta are standing waves. To conlcude, the band structure is calculated from the central equation and compared to the numerically exact band structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

Here, we introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Enhancing the accuracy of XPS calculations: Exploring hybrid basis set schemes for CVS-EOMIP-CCSD calculations

Reliable computational methodologies and basis sets for modeling x-ray spectra are essential for extracting and interpreting electronic and structural information from experimental x-ray spectra. In particular, the trade-off between numerical accuracy and computational cost due to the size of the basis set is a major challenge, since molecular orbitals undergo extreme relaxation in the core-hole state. To gain clarity on the changes in electronic structure induced by the formation of a core-hole, the use of sufficiently flexible basis for expanding the orbitals, particularly for the core region, has been shown to be essential. This work focuses on the refinement of core-hole ionized state calculations using the equation-of-motion coupled cluster family of methods through an extensive analysis on the effectiveness of “hybrid” and mixed basis sets. In this investigation, we utilize the CVS-EOMIP-CCSD method in combination and construct hybrid basis sets piecewise from readily available Dunning’s correlation consistent basis sets in order to calculate x-ray ionization energies (IEs) for a set of small gas phase molecules. Our results provide insights into the impact of basis sets on the CVS-EOMIP-CCSD calculations of K-edge IEs of first-row p-block elements. Furthermore, these insights enable us to understand more about the basis set dependence of the core IEs computed and allow us to establish a protocol for deriving reliable and cost-effective theoretical estimates for computing IEs of small molecules containing such elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Impact of Integration Scheme on Performance of Anisotropic Plasticity Models

Given the prevalent role of metals in a variety of industries, schemes to integrate corresponding constitutive models in finite element applications have long been studied. A number of formulations have been developed to accomplish this task; each with their own advantages and costs. Often the focus has been on ensuring the accuracy and numerical stability of these algorithms to enable robust integration. While important, emphasis on these performance metrics may often come at the cost of computational expense potentially neglecting the needs of individual problems. In the current work, the performance of two of the most common integration methods for anisotropic plasticity -- the convex cutting plane (CCP) and closest point projection (CPP) -- across a variety of metrics is assessed; including accuracy and cost. A variety of problems are considered ranging from single elements to large representative simulations including both implicit quasistatic and explicit transient dynamic type responses. The relative performance of each scheme in the different instances is presented with an eye towards guidance on when the different algorithms may be beneficial.

36 MATERIALS SCIENCE↗