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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Multicomponent Reactive Transport Model for Integrated Surface‐Subsurface Hydrology Problems

Abstract Despite the widespread use of integrated hydrology models in a variety of applications, consideration of multicomponent reactive transport is still not common. The implementation of these processes requires coupling transport at the surface‐subsurface interface and efficient solution of the non‐linear geochemical model that is consistent with the integrated hydrology solution. The Advanced Terrestrial Simulator provides a flexible multiphysics framework that facilitated this process. In this work, the integrated reactive transport process kernel (PK) was weakly coupled to the integrated hydrology PK. In turn, integrated transport and reactions were coupled using an operator splitting approach. This splitting enabled an explicit solution of the integrated transport problem, including a novel algorithm to calculate exchange fluxes across the surface‐subsurface interface and a point‐by‐point solution of the geochemical problem. Geochemical capabilities were added using well‐established external codes, but rather than using a custom interface to each, a generic interface was used that clearly specifies the variables and operations used by the chemistry PK. The implementation is demonstrated with two example simulations: transport of a tracer in a soil column as it saturates over time and water ponds on the surface and reactive transport in a hillslope driven by successive wet‐dry cycles that result in infiltration, runoff and exfiltration processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗
DOE OSTI2022

An investigation of the multi-mode Richtmyer-Meshkov instability at a gas/HE interface using Pagosa

Here, in this work, we present a hydrocode Pagosa and explore the Richtmyer-Meshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagration-to-detonation transition (DDT) process in future. In Pagosa, spatial discretization is implemented on cubic staggered grids by computing different variables at the vertex and the cell center, respectively, a special operator-splitting technique is employed to reduce the computational cost, and an artificial viscosity is added to handle the discontinuous shock waves in our simulations. To quantitatively evaluate the capability of Pagosa to solve these kinds of instabilities, the single mode Rayleigh-Taylor instability (RTI) and the multimode RMI at an air/SF 6 interface are first performed, respectively. The Pagosa results are compared with the related numerical solutions in the existing references and the experimental result. Moreover, a theoretical derivation of growth of RTI is also provided based on our numerical method. Subsequently, we explore the multi-mode RMI at an air/HE interface as well as the effects of several factors using Pagosa. Numerical results show that Pagosa is a powerful toolset to generate the right structures and the amplitude of RTI and RMI at an air/SF 6 interface. The solid HE can be penetrated by a strong shock wave and forms RMI deformations. The RMI at an air/HE interface behaves very different than at an air/SF 6 interface, periodic, decreased oscillation is observed due to material character, and is very sensitive to the initial simulation settings, that is, a tiny change in physical quantities will lead to a remarkable RMI structure, which is also observed in a shock bubble interaction. The findings in this work are significant, and will present a new insight for the high explosive field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗
DOE OSTI2025

A discontinuous Galerkin spectral element method for compressible reacting flows

High-order methods have recently been shown to be an effective tool for high-fidelity flow computations like direct numerical simulations and large-eddy simulations because of their strong balance between accuracy and computational cost. In this work, a high-order discontinuous Galerkin spectral element method (DGSEM) is developed to solve the chemically reacting Navier-Stokes equations. To handle the disparate length and time scales associated with these equations, we develop a novel method which combines the spectral accuracy of the SEM with the flexibility of the DG approach. The framework, implemented in the spectral element code Nek5000, is well suited to capture turbulence in smooth regions of the flow, while maintaining numerical stability in the presence of shocks. An entropy-residual based artificial viscosity is added to smooth shocked regions of flow, and a positivity-preserving limiter is implemented to suppress non-physical oscillations. These enhancements support the numerical stability of the hydrodynamic sub-step, which is decoupled from the chemistry integration through a second-order operator splitting method. Here, a series of smooth and discontinuous validation cases are presented in increasing physical and computational complexity for both inviscid and viscous flows. In particular, simulations of canonical one-dimensional and two-dimensional detonations are performed, and the high-order numerical results are validated against available literature data. Additional validation studies are carried out for classical three-dimensional numerical simulations of incompressible and compressible turbulent flows.

Compressible reacting flows↗
DOE OSTI2025

Chemical timescale effects on detonation convergence

Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next- generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, the objective of this work is to provide a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an AMReX-based adaptive mesh refinement flow solver-which enables resolutions up to ($\mathcal{O}$ (1000) cells-per-induction length-the convergence analysis is conducted using two kinetics configurations: (1) the simplified three-step Arrhenius-based model mechanism of Short and Quirk (1997), where chemical timescales in the detonation are modified by adjusting activation energies in the initiation and branching reactions, and (2) a detailed hydrogen- air mechanism, where the chemical timescales are adjusted by varying the ambient pressure. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and wave speeds) and microscopic (wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. In particular, chemical timescale reductions were found to have minimal impact on the convergence of macroscopic properties. Furthermore, analyses of microscopic convergence trends, particularly in the reaction front location, revealed a key insight: maintaining the induction time while eliminating prohibitive chemical timescales through mechanism simplifications and combustion modeling can significantly enhance detonation convergence properties. Ultimately, this work uncovers resolution-dependent unsteady detonation convergence regimes and highlights the important role played by not only the chemical timescales, but also the ratio between the chemical timescale and induction time on the numerical convergence of the detonation wave structure.

Adaptive mesh refinement↗
DOE OSTI2022

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

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

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 10 23 W/cm 2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. Here we present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Data transfers for full core heterogeneous reactor high- fidelity multiphysics studies

Multiphysics simulations for nuclear reactor analysis are usually performed by resorting to operator splitting and fixed point iterations between single-physics solvers. This enables the separate solution of each physics, such as neutronics, fuel performance, and thermal hydraulics, on meshes tailored to the requirements of the respective numerical discretizations of the equations. As the equations are coupled, several fields must be transferred between single-physics solves. Projecting fields between meshes while preserving order of accuracy, conservation properties, and mapping non-overlapping geometries is a complex endeavor. This conference paper will present the transfers as implemented in MOOSE, which can handle arbitrary meshes, arbitrary mappings, conservation of integral quantities, and are made to scale with distributed simulations on both ends of the transfers. Their adequacy for advanced nuclear reactor multiphysics coupling is shown through examples and numerical studies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implicit full-F simulations of neoclassical ion transport

The development of implicit time integration capabilities for axisymmetric full-F continuum simulations of ion neoclassical transport is reported. The approach involves the implicit treatment of the gyrokinetic Vlasov equation coupled to the nonlinear Fokker–Planck collision model in the long-wavelength limit approximation. To facilitate implicit simulations, advanced preconditioning of individual physics operators is developed, and a global multi-physics preconditioner is constructed by adopting an operator splitting methodology. The algorithm is implemented in the finite-volume code COGENT and is applied to study neoclassical transport properties for both the main ion species and the lithium impurity species in the closed-field-line region of the LTX- β tokamak. The implicit COGENT simulations elucidate the role of non-local transport effects, while demonstrating substantial speedup over the corresponding explicit approach.

Dorf, Mikhail [Lawrence Livermore National Laborat↗
DOE OSTI2020

Iterative X-ray spectroscopic ptychography

Spectroscopic ptychography is a powerful technique to determine the chemical composition of a sample with high spatial resolution. In spectro-ptychography, a sample is rastered through a focused X-ray beam with varying photon energy so that a series of phaseless diffraction data are recorded. Each chemical component in the material under investigation has a characteristic absorption and phase contrast as a function of photon energy. Using a dictionary formed by the set of contrast functions of each energy for each chemical component, it is possible to obtain the chemical composition of the material from high-resolution multi-spectral images. This paper presents SPA (spectroscopic ptychography with alternating direction method of multipliers), a novel algorithm to iteratively solve the spectroscopic blind ptychography problem. First, a nonlinear spectro-ptychography model based on Poisson maximum likelihood is designed, and then the proposed method is constructed on the basis of fast iterative splitting operators. SPA can be used to retrieve spectral contrast when considering either a known or an incomplete (partially known) dictionary of reference spectra. By coupling the redundancy across different spectral measurements, the proposed algorithm can achieve higher reconstruction quality when compared with standard state-of-the-art two-step methods. It is demonstrated how SPA can recover accurate chemical maps from Poisson-noised measurements, and its enhanced robustness when reconstructing reduced-redundancy ptychography data using large scanning step sizes is shown.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

A Hybrid Finite-Volume, Discontinuous Galerkin Discretization for the Radiative Transport Equation

In this report we propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite-volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.

97 MATHEMATICS AND COMPUTING↗