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At least 127 records · Page 7
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DOE OSTI2020

Comparison of momentum transport models for numerical relativity

The main problems of nonvacuum numerical relativity, compact binary mergers and stellar collapse, involve hydromagnetic instabilities and turbulent flows, so that kinetic energy at small scales leads to mean effects at large scale that drive the secular evolution. Notable among these effects is momentum transport. We investigate two models of this transport effect, a relativistic Navier-Stokes system and a turbulent mean stress model, that are similar to all of the prescriptions that have been attempted to date for treating subgrid effects on binary neutron star mergers and their aftermath. Our investigation involves both stability analysis and numerical experimentation on star and disk systems. We also begin the investigation of the effects of particle and heat transport on postmerger simulations. Here, we find that correct handling of turbulent heating is crucial for avoiding unphysical instabilities. Given such appropriate handling, the evolution of a differentially rotating star and the accretion rate of a disk are reassuringly insensitive to the choice of prescription. However, disk outflows can be sensitive to the choice of method, even for the same effective viscous strength. We also consider the effects of eddy diffusion in the evolution of an accretion disk and show that it can interestingly affect the composition of outflows.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Electroconvection near an ion-selective surface with Butler–Volmer kinetics

We study the effects of interfacial kinetics on the electro-hydrodynamics of ion transport near an ion-selective surface using a combination of linear stability analysis and numerical simulation. The finite kinetics of the electrolyte–electrode interface affects the ion transfer and electroconvection in many ways. On a surface of fixed topography, such as a metal surface of slow and stable ion deposition or covered by a polymer membrane, the finite kinetics reduces the current in one-dimensional ion diffusion/migration, increases the critical voltage for the onset of the electroconvective instability, changes the dynamics of the electroconvection and the overlimiting current, and enhances the lateral ion diffusion within the interfacial layer. The first three effects are indirectly caused by the reaction kinetics and can be characterized by an effective voltage difference across the liquid electrolyte. In comparison, the last effect is controlled by a direct interplay between kinetics and nonlinear electroconvection. Scaling laws for ion transport and features of electroconvection are proposed. We also analyse the linear stability of a surface which evolves under ion deposition and find that the finite kinetics decreases the growth rate of both electroconvective and morphological instabilities and therefore modifies the wavenumber of the most unstable mode.

Mechanics↗
DOE OSTI2021

Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron-frequency compressional Alfvén eigenmodes (CAEs) and global Alfvén eigenmodes (GAEs) in low-aspect-ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam powers in NSTX experiments, prompting a further examination of the conditions necessary for their excitation. Linear simulations have been performed with the hybrid MHD–kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Additionally, three distinct types of modes were found in the simulations—co-CAEs, cntr-GAEs, and co-GAEs—with differing spectral and stability properties. The simulations revealed that unstable GAEs are more ubiquitous than unstable CAEs, which is consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from the simulations and analytically estimated for relevant sources absent from the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hybrid simulations of sub-cyclotron compressional and global Alfven Eigenmode stability in spherical tokamaks

A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfven Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes are found in simulations -- co-CAEs, cntr-GAEs, and co-GAEs -- with differing spectral and stability properties. The simulations reveal that unstable GAEs are more ubiquitous than unstable CAEs, consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from simulations and estimated analytically for relevant sources not present in the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

Compressional Alfven Eigenmodes↗
DOE OSTI2020

An ideal MHD δW stability analysis that bypasses the Newcomb equation

In the following work, we demonstrate the efficacy of a Riccati δW ideal MHD stability analysis that bypasses the numerically intractable integration of the Newcomb equation. By transforming the linear Newcomb equation into a quadratic Riccati equation, an accurate and equivalent δW analysis is performed that is shown to enjoy some numerical advantages. Additionally, we demonstrate that the Riccati approach is better conditioned than its Newcomb counterpart at the magnetic axis, and we apply dynamical systems insights to examine its behavior at singular points. We further discuss the constraints involved in solving for the extremal admissible perturbations of a δW analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Refining the GENEVA method for Higgs boson production via gluon fusion

We describe a number of improvements to the Geneva method for matching NNLO calculations to parton shower programs. In particular, we detail changes to the resummed calculation used in the matching procedure, including disentangling the cross section dependence on factorisation and beam scales, and an improved treatment of timelike logarithms. We also discuss modifications in the implementation of the splitting functions which serve to make the resummed calculation differential in the higher multiplicity phase space. These changes improve the stability of the numerical cancellation of the nonsingular term at small values of the resolution parameter. As a case study, we consider the gluon-initiated Higgs boson production process gg → H. We validate the NNLO accuracy of our predictions against independent calculations, and compare our showered and hadronised results with recent data taken at the ATLAS and CMS experiments in the diphoton decay channel, finding good agreement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Signatures of ambient pressure superconductivity in thin film La 3 Ni 2 O 7

Recently, the bilayer nickelate La 3 Ni 2 O 7 has been discovered as a new superconductor with transition temperature T c near 80 K under high pressure. Despite extensive theoretical and experimental work to understand the nature of its superconductivity, the requirement of extreme pressure restricts the use of many experimental probes and limits its application potential. Here, in this work, we present signatures of superconductivity in La 3 Ni 2 O 7 thin films at ambient pressure, facilitated by the application of epitaxial compressive strain. The onset T c varies approximately from 26 K to 42 K, with higher T c values correlating with smaller in-plane lattice constants. We observed the co-existence of other Ruddlesden-Popper phases within the films and dependence of transport behavior with ozone annealing, suggesting that the observed low zero resistance T c of around 2 K can be attributed to stacking defects, grain boundaries, and oxygen stoichiometry. This finding initiates numerous opportunities to stabilize and study superconductivity in bilayer nickelates at ambient pressure, and to facilitate the broad understanding of the ever-growing number of high temperature and unconventional superconductors in the transition metal oxides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Feasibility of an experiment on clumping induced by the Crow instability along a shocked cylinder

The growth of three-dimensional perturbations subject to the Crow instability along a vortex dipole resulting from the passage of a shock wave through a heavy gaseous cylinder is examined numerically. A linear stability analysis is performed based on geometric parameters extracted from two-dimensional simulations to determine the range of unstable wavenumbers, which is found to extend from 0.0 to 1.3 when normalized by the core separation distance. The analysis is then verified by comparison to three-dimensional simulations, which clearly show the development of the instability and the pinch-off of the vortex dipole into isolated vortex rings, which manifest as clumps of the original cylinder material. A scaling law is developed to determine the relevant spatiotemporal scales of the instability development, which is then used to assess the feasibility of a high-energy-density experiment visualizing clump formation. Specifically, a shocked cylinder with an initial diameter of 100 μm consisting of a perturbation of approximate wavelength and amplitude of 600 and 10 μm, respectively, is expected to form clumps resulting from the Crow instability approximately 40 ns after it is shocked, with dynamics which can be readily visualized on the Omega EP laser facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

${\tt Warm}$SPy: a numerical study of cosmological perturbations in warm inflation

We present ${\tt Warm}$SPy, a numerical code in Python designed to solve for the perturbations' equations in warm inflation models and compute the corresponding scalar power spectrum at CMB horizon crossing. In models of warm inflation, a radiation bath of temperature T during inflation induces a dissipation (friction) rate of strength Q ∝ T c /Φ m in the equation of motion for the inflaton field Φ. While for a temperature-independent dissipation rate (c = 0) an analytic expression for the scalar power spectrum exists, in the case of a non-zero value for c the set of equations can only be solved numerically. For c > 0 (c < 0), the coupling between the perturbations in the inflaton field and radiation induces a growing (decaying) mode in the scalar perturbations, generally parameterized by a multiplicative function G(Q) which we refer to as the scalar dissipation function. Using ${\tt Warm}$SPy, we provide an analytic fit for G(Q) for the cases of c = {3,1,-1}, corresponding to three cases that have been realized in physical models. Compared to previous literature results, our fits are more robust and valid over a broader range of dissipation strengths Q ϵ [10 -7 ,10 4 ]. Additionally, for the first time, we numerically assess the stability of the scalar dissipation function against various model parameters, inflationary histories as well as the effects of metric perturbations. As a whole, the results do not depend appreciably on most of the parameters in the analysis, except for the dissipation index c, providing evidence for the universal behaviour of the scalar dissipation function G(Q).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport

We apply Cattaneo's relaxation approach to the one-dimensional coupled Boussinesq groundwater flow and advection-diffusion-reaction equations, commonly used in engineering applications to simulate contaminant transport in the subsurface. The diffusion-type governing equations are reformulated as a hyperbolic system, augmented by an equation that can be interpreted as a momentum balance. The hyperbolization enables an efficient unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. An augmented Roe scheme is used to solve the hyperbolic system. The hyperbolized system of equations is studied in a set of steady state and transient test cases with idealized geometry. These test cases confirm the equivalence of the hyperbolic system to its original formulation. The larger time step size of the hyperbolic equation is verified theoretically by means of a stability analysis and numerically in the test cases. Finally, a reach-scale application of flow and transport across a river meander is considered. This application case shows that the performance of the hyperbolic relaxation approach holds for more realistic groundwater flow and transport problems, relevant to water resources management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

High-Fidelity, Low-Dissipation/Symmetry-Preserving Numerical Scheme for Solving the Euler Equations with Unstructured, Metric-Based Mesh Adaptation

This work presents an overview of a high-fidelity compressible Euler solver that utilizes the continuous Galerkin (CG) method with added artificial numerical diffusion for stabilization to solve a variety of unsteady and steady benchmark inviscid flow problems. This work shows that discretizing the Euler equations with this CG approach and first order basis functions produces a cost-effective stencil as well as simple well-posed boundary conditions. We show through convergence testing with manufactured solutions that the reduced stencil of CG, combined with the low amount of artificial diffusion required when using the stabilization method outlined in this work, leads to stable and highly accurate results for a variety of unsteady and steady applications. When combined with the adaptive mesh refinement approach used for many of the cases in this work, our results show that the flow solver achieves even more accurate results. A variety of inviscid flow cases are presented in this work, including transient 2D cases with complex shock structures and several steady 3D airfoils sections with a constant span.

Doetsch, Kevin [ORNL] (ORCID:0000000267051705)↗
DOE OSTI2023

Numerical Analysis of Regular Material Point Method and its Application to Multiphase Flows

The material point method (MPM) is gaining wide popularity in engineering research to model and simulate complex multiphase flow dynamics. The method relies on solving the governing equations of motion and transport in a Lagrangian framework using particles also known as material points. The fluid and kinematic properties are stored on the material points while the spatial gradient calculation and temporal integration are performed on a background grid. This Lagrangian framework allows for large deformations, easy integration of constitutive models, and direct import of complex geometries as particles. However, despite their increasing popularity, very few studies have addressed the issues of numerical resolution and stability of MPM techniques. The presence of additional factors such as the number of material points-per-cell, the location of the material points, the CFL-like condition used in time update, and the grid shape functions also increase the complexity of the error analysis when compared to other finite element methods. In this presentation, we analyze the various forms of error incurred in the application of MPM to continuum mechanics and multiphase flows. The effect of the previously mentioned factors on the error dynamics is studied. The application of these principles to canonical and industrial problems is also presented.

high pressure reverse osmosis↗
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a novel stability analysis method and provide sufficient conditions of DMM's stochastic stability. The proposed stability analysis is based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation function on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Drgona, Jan↗
DOE OSTI2023

Comparison of MHD stability properties between QH-mode and ELMy H-mode plasmas by considering plasma rotation and ion diamagnetic drift effects

Magnetohydrodynamic (MHD) stability at tokamak edge pedestal in a quiescent H-mode (QH-mode) and type-I ELMy H-mode plasmas in DIII-D experiment was analyzed by considering plasma rotation and ion diamagnetic drift effects. QH-mode plasma is marginally stable to kink/peeling mode (K/PM), but ELMy H-mode one is almost unstable to peeling-ballooning mode (PBM). It was identified that there are three physics features responsible for the difference in the MHD stability properties between QH-mode plasma and ELMy H-mode one. These are the distance of pedestal foot from the last closed flux surface (LCFS), the amount of the ion diamagnetic drift frequency at pedestal, and impact of coupled rotation and ion diamagnetic drift effects. These features were confirmed through the numerical experiments that the stability properties of the QH-mode plasma can be changed to that of the ELMy H-mode one by shifting the plasma profiles inward in the radial direction and halving the ion diamagnetic drift frequency. The reasons of the change in the stability properties are thought as that K/PM is stabilized due to the inward shift of the bootstrap current profile, and PBM is destabilized due to the reduction of the coupled rotation and ion diamagnetic drift stabilizing effect. Importance of these features was validated through numerical experiments with experimental data of other QH-mode plasmas in DIII-D. All the results show that MHD stability properties of QH-mode plasma can be obtained in case that pedestal foot is close to LCFS, ion diamagnetic drift frequency is large due to high ion temperature, and strong rotation shear exists near pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory

We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by 'ideal interfaces', and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient $\nabla p = 0$. The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the $\nabla p = 0$ in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion6 101; Glasser et al 1975 Phys. Fluids18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.

59 BASIC BIOLOGICAL SCIENCES↗