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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Coupling Approaches with Non-matching Grids for Classical Linear Elasticity and Bond-based Peridynamic Models in 1D

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. Further, the effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Mesh refinement for anisotropic diffusion in magnetized plasmas

Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. Here, this work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗
DOE OSTI2023

Towards critical and supercritical electromagnetic fields

Abstract The availability of ever stronger, laser-generated electromagnetic fields underpins continuing progress in the study and application of nonlinear phenomena in basic physical systems, ranging from molecules and atoms to relativistic plasmas and quantum electrodynamics. This raises the question: how far will we be able to go with future lasers? One exciting prospect is the attainment of field strengths approaching the Schwinger critical field ${E}_{\mathrm{cr}}$ in the laboratory frame, such that the field invariant ${E}^2-{c}^2{B}^2>{E}_{\mathrm{cr}}^2$ is reached. The feasibility of doing so has been questioned, on the basis that cascade generation of dense electron–positron plasma would inevitably lead to absorption or screening of the incident light. Here we discuss the potential for future lasers to overcome such obstacles, by combining the concept of multiple colliding laser pulses with that of frequency upshifting via a tailored laser–plasma interaction. This compresses the electromagnetic field energy into a region of nanometre size and attosecond duration, which increases the field magnitude at fixed power but also suppresses pair cascades. Our results indicate that laser facilities with peak power of tens of PW could be capable of reaching ${E}_{\mathrm{cr}}$ . Such a scenario opens up prospects for the experimental investigation of phenomena previously considered to occur only in the most extreme environments in the universe.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Wavelength scaling and multicolor operation of a plasma-driven attosecond x-ray source via harmonic generation

The generation of high-power coherent soft x-ray pulses of sub-100 as duration and 10 nm wavelength using beams from a GeV energy plasma wakefield accelerator has been recently investigated in Emma []. As a future upgrade to this concept, this contribution investigates scaling to shorter x-ray wavelengths by cascading undulators tuned to higher harmonics of the fundamental. We present two simulation studies for plasma-driven attosecond harmonic generation schemes with final photon wavelengths of 2 and 0.40 nm. We demonstrate in these schemes that using undulators with retuned fundamental frequencies can produce GW-scale pulses of sub-nm radiation with tens of attosecond-scale pulse lengths, an order of magnitude shorter than current state-of-the-art attosecond x-ray free electron lasers (XFELs). This multipulse multicolor operation will be broadly applicable to attosecond pump-probe experiments. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Uncovering extreme nonlinear dynamics in solids through time-domain field analysis

Time-domain analysis of harmonic fields with sub-cycle resolution is now experimentally viable due to the emergence of sensitive, on-chip techniques for petahertz-scale optical-field sampling. We demonstrate how such a time-domain, field-resolved analysis uncovers the extreme nonlinear electron dynamics responsible for high-harmonic generation within solids. Time-dependent density functional theory was used to simulate harmonic generation from a solid-state band-gap system driven by near- to mid-infrared waveforms. Particular attention was paid to regimes where both intraband and interband emission mechanisms play a critical role in shaping the nonlinear response. We show that a time-domain analysis of the harmonic radiation fields identifies the interplay between intra- and interband dynamical processes underlying the nonlinear light generation. With further analysis, we show that changes to the dominant emission regime can occur after only slight changes to the peak driving intensity and central driving wavelength. Furthermore, time-domain analysis of harmonic fields also reveals, for the first time, the possibility of rapid changes in the dominant emission mechanism within the temporal window of the driving pulse envelope. Finally, we examine the experimental viability of performing time-domain analysis of harmonic fields with sub-cycle resolution using realistic parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Light-Matter Interaction near the Schwinger Limit Using Tightly Focused Doppler-Boosted Lasers

Strong-field quantum electrodynamics (SF QED) is a burgeoning research topic dealing with electromagnetic fields comparable to the Schwinger field (≈1.32×10 18 V/m). While most past and proposed experiments rely on reaching this field in the rest frame of relativistic particles, the Schwinger limit could also be approached in the laboratory frame by focusing to its diffraction limit the light reflected by a plasma mirror irradiated by a multipetawatt laser. Here, we explore the interaction between such intense light and matter with particle-in-cell simulations. We find that the collision with a relativistic electron beam would enable the study of the nonperturbative regime of SF QED, while the interaction with a solid target leads to a profusion of SF QED effects that retroact on the interaction. In both cases, relativistic attosecond pair jets with high densities are formed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High-Performance Electron Sources: Numerical Methods and Beam Dynamics at the Precision Frontier

Electron sources have a wide range of applications and there are many stakeholders that express continuing need for improvements and performance enhancements. Whether we consider ultra-cold, high-brightness, high-charge or high-average current source needs, there are some common themes from the point of view of the beam dynamics involved. These are the following ones: ability to model accurately the emission processes, including the presence of often complicated cathode and other boundary surfaces with a wide range of spatial scales; ability to deal accurately and efficiently with a large number of particles interacting pair-wise, including the stochastic part of these interactions with a wide range of spatial scales; and ability to propagate the particle distributions in time, including collisions with a wide range of temporal scales. These tasks require high precision and accuracy since the goal is usually generation, transport and preservation of very high-quality beams. This grant addressed one of the rem

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

A guide to the design of the virtual element methods for second- and fourth-order partial differential equations

Here we discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material. The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. Inspired by, we develop a new conforming VEM for the discretization of the two equations, which is implementation-friendly, i.e., different terms can be implemented by exploiting a single projection operator. We use C 0 and C 1 virtual elements for the second-and fourth-order partial differential equation, respectively. For both equations, we review the formulation of the virtual element approximation and discuss the details pertaining the implementation.

42 ENGINEERING↗
NASA NTRS2004

Nonlinear optics and crystalline whispering gallery mode resonators

We report on our recent results concerning fabrication of high-Q whispering gallery mode (WGM) crystalline resonators, and discuss some possible applications of lithium niobate WGM resonators in nonlinear optics and photonics. In particular, we demonstrate experimentally a tunable third-order optical filter fabricated from the three metalized resonators; and report observation of parametric frequency dobuling in a WGM resonator made of periodically poled lithium niobate (PPLN).

whispering gallery mode↗
NASA NTRS2020

Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier–Stokes Equations

In this paper, we extend the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, we utilize a computationally simple and efficient approach based upon using decoupled interpolation operators. The resulting scheme is entropy conservative/stable and elementwise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation con firm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence), which are comparable to those of the original conforming scheme. Simulations of the Taylor{Green vortex at R(e) = 1,600 and turbulent flow past a sphere at R(e(infinity)) = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h=p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme.

Nonconforming interfaces↗
NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗
NASA NTRSDate not supplied

Turbulent Simulations of Cooling Jets in Crossflow

Turbulent flow simulations were completed of the THX-III single hole film cooling experiment performed at NASA Glenn Research Center (GRC). Two different Large-Eddy Simulation (LES) approaches were completed along with a RANS based study. The first LES approach utilizes the Flux Reconstruction (FR) based finite element code GFR, while the second approach makes use of the compact difference solver FDL3DI. Both LES codes were run on grids larger than 1.5 Billion degrees of freedom (DoF). The RANS simulations used FUN3D and included a grid convergence as a turbulence closure study. A summary of the computational approaches and key findings are presented along with the experimental measurements. Significant progress has been made towards the completion of this work, as all but one simulation have been completed. The preliminary findings have shown the LES approaches have excellent agreement with each other, and closely follow the trends of the experiment. The Reynolds stress RANS closure, while the best of the RANS results, had difficulty matching the results of the LES and experimental measurements.

High-Order Methods↗
NASA NTRSDate not supplied

Implicit Large-Eddy Simulation of Single-Injector Cooling Flow

The turbulent heat flux vector plays a critical role in aero-propulsion flow. Currently, traditional RANS based methods do not currently have reliable closures which can accurately predict the turbulent transport of heat. Scale Resolving Simulations can provide critical insight into this fundamental fluid mechanism. Large-eddy Simulations (LES) were performed on the single-hole film-cooling experimental configuration from the recent experiments conducted at NASA Glenn Research Center (GRC)[1]. The experiment of Wernet et al. obtained mean and fluctuating temperatures which can be used to validate LES results predicting the turbulent heat flux vector. The FDL3DI flow solver was used to complete simulations of two blowing ratios of the THX - III dataset. A grid sensitivity study was also performed. Initial LES results show promising agreement between the simulation and experimental measurements.

High-Order methods↗