Search NASA⌕ Search

SEARCH · Search NASA

Results for “Semi-implicit”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Verification of an energy-conserving semi-implicit electrostatic particle-in-cell scheme for modeling high-density plasma at scale

A verification study of a semi-implicit energy-conserving electrostatic particle-in-cell algorithm is presented. The algorithm relaxes the time-step and mesh-size constraints that require resolution of the plasma period and Debye length associated with traditional explicit momentum-conserving particle-in-cell algorithms. Physical implications and applicability of using the semi-implicit scheme for modeling high-density plasmas are discussed. Where possible, numerical results are compared against analytical solutions. The simulation results indicate that the algorithm is stable at time steps larger than twice the inverse plasma frequency and cell sizes larger than the Debye length. It is found that the algorithm gives adequate results, provided that the distribution function and the spatiotemporal scales dictating the physics of the problem are resolved. As such, the algorithm may provide a robust method for kinetic modeling of high-density plasmas at scale.

Cyclotron resonance↗
DOE OSTI2025

Planar Collisionless Shock Simulations with the Semi-implicit Particle-in-cell Model FLEKS

This study investigates the applicability of the semi-implicit particle-in-cell code FLexible Exascale Kinetic Simulator (FLEKS) to heliospheric shock simulations. We examine one- and two-dimensional local planar shock simulations, initialized using MHD states with upstream conditions representative of plasmas in the hypersonic, β ∼ 1 regime, for both quasi-perpendicular and quasi-parallel configurations. The refined algorithm in FLEKS proves robust, enabling accurate shock simulations with a grid resolution on the order of the electron inertial length d e . Our simulations successfully capture key shock features, including shock structures (foot, ramp, overshoot, and undershoot), upstream and downstream waves (fast magnetosonic, whistler, Alfvén ion-cyclotron, and mirror modes), and non-Maxwellian particle distributions. Crucially, we find that at least two spatial dimensions are critical for accurately reproducing downstream-wave physics in quasi-perpendicular shocks and capturing the complex dynamics of quasi-parallel shocks, including surface rippling, shocklets, short, large-amplitude magnetic structures, magnetic reconnection, and jets. Furthermore, our parameter studies demonstrate the impact of mass ratio and grid resolution on shock physics. This work provides valuable guidance for selecting appropriate physical and numerical parameters for shock simulations using a semi-implicit PIC method, paving the way for incorporating kinetic shock processes into large-scale collisionless plasma simulations with the MHD-AEPIC model.

plasma astrophysics↗
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↗
NASA NTRS1979

A fast semi-implicit algorithm for problems of mixed type

Certain physical processes are modeled by partial differential equations which are parabolic over part of the domain and elliptic over the remainder. A family of semi-implicit algorithms which are well suited to initial-boundary value problems of this mixed type is discussed. One important feature of these algorithms is the use of an approximate inverse for the solution of the implicit linear system. A strong error analysis results in an estimate of the total error as a function of approximate inverse error e and time step h.

Frederickson, P. O.↗
DOE OSTI2025

Semi-implicit continuum kinetic modeling of weakly collisional parallel transport in a magnetic mirror

We present implicit-explicit (IMEX) kinetic simulations of weakly collisional parallel plasma transport in magnetic mirror configurations using the continuum code COGENT. The numerical scheme employs a Jacobian-free Newton–Krylov method with algebraic multigrid preconditioning to overcome the severe time step limitations imposed by strong mirror forces in fully explicit schemes. Applied to parameters relevant to the Wisconsin HTS Axisymmetric Mirror experiment, the IMEX approach enables time steps up to 2.5×10 4 times larger than those permitted by explicit methods, resulting in a 2500× speedup in 1D–2V simulations of parallel transport with kinetic ions and Boltzmann electrons. Additionally, a reduced bounce-averaged model for a square mirror is implemented to support the computationally intensive fully kinetic simulations. The bounce-averaged formulation is used to evaluate the numerical convergence of the velocity-space discretization algorithms and to assess the role of the collision model by comparing simulations employing the nonlinear Fokker–Planck and the simplified Lenard–Bernstein–Dougherty collision operators.

Collision theories↗
DOE OSTI2025

GPU-accelerated kinetic Hall thruster simulations in WarpX

Abstract Two-dimensional (axial-azimuthal) simulations of a Hall thruster are performed using the open-source particle-in-cell code WarpX. The simulation conditions are chosen to match those of the axial-azimuthal benchmark first reported by Charoy et al. in 2019. A range of numerical and solver parameters is investigated in order to find those which yield the best performance. It is found that WarpX completes the benchmark case in 3.8 days on an Nvidia V100 GPU, and in as low as 1.5 days on a more recent Nvidia H100 GPU. Of the numerical parameters investigated, it is determined that the field-solve tolerance and particle resampling thresholds have the largest effect on the simulation wall time and that particle resampling may artificially widen electron velocity distribution functions, leading to unphysical heating. A semi-implicit scheme for the electrostatic field solve is tested and is found to produce results consistent to within 10% of the benchmark in less than twelve hours. The scaling properties of the electrostatic solver to multiple GPUs are also assessed on a uniform plasma test problem. The results of this work are discussed in the context of advancements in GPU hardware and the suitability of kinetic Hall thruster simulations for engineering applications.

Marks, Thomas A.↗
DOE OSTI2025

An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models

Here, we propose an efficient end-to-end deep learning method for solving nonlocal Allen–Cahn (AC) and Cahn–Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, predictive capabilities, and cost reductions of the proposed method.

42 ENGINEERING↗
DOE OSTI2026

Fast solvers for tokamak fluid models with PETSc

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. In this work we develop the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the M3D-C1 (https://m3dc1.pppl.gov) fusion energy science code. The semi-implicit time integrator in M3D-C1 is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in M3D-C1 is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in M3D-C1 is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC (https://cfs.energy/technology/sparc) disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Moment-based adaptive time integration for thermal radiation transport

Here, in this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2026

Simulation of electron Bernstein waves using FullWave with a 2D non-local hot plasma model

Hot plasma wave simulation capability is expanded in the FullWave code by updating the hybrid iterative solver in the code with a semi-implicit time stepping method. The new approach is used to simulate Electron Bernstein Wave (EBW) heating in over-dense spherical tokamak plasmas. The code’s hybrid iterative solver circumvents the prohibitive memory cost of direct methods by combining a time evolution of Maxwell’s equations with frequency-domain relaxation, while the conductivity kernel, calculated via 3D particle tracking, captures the essential non-local wave–particle interactions. One-dimensional EBW simulations verify the algorithm’s accuracy by demonstrating mode conversion from X-mode wave to EBW at the upper hybrid resonance and a strong cyclotron damping near the plasma core. Two-dimensional simulation reproduces the predicted short EBW wavelength and quantitatively matches the hot-plasma dispersion relation. This study demonstrates the fidelity of the hybrid solver for the electron cyclotron frequency range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Swift

Swift is a fast Fourier transform based spectral solver based on the MOOSE framework. It supports GPU accelerated semi-implicit solves of partial differential equations, such as those used for phase field mesoscale microstructure evolution.

Schwen, Daniel [Idaho National Laboratory (INL), I↗
NASA NTRS1976

Numerical simulation of turbulent jet noise, part 2

Results on the numerical simulation of jet flow fields were used to study the radiated sound field, and in addition, to extend and test the capabilities of the turbulent jet simulation codes. The principal result of the investigation was the computation of the radiated sound field from a turbulent jet. In addition, the computer codes were extended to account for the effects of compressibility and eddy viscosity, and the treatment of the nonlinear terms of the Navier-Stokes equations was modified so that they can be computed in a semi-implicit way. A summary of the flow model and a description of the numerical methods used for its solution are presented. Calculations of the radiated sound field are reported. In addition, the extensions that were made to the fundamental dynamical codes are described. Finally, the current state-of-the-art for computer simulation of turbulent jet noise is summarized.

Metcalfe, R. W.↗
NASA NTRS1975

Some examples of unsteady transonic flows over airfoils

A finite difference flutter analysis is presented for the NACA 64A-410 airfoil at M equals 0.72, where the incidence is abruptly changed from 2 to 4 degrees. The effect of gust loads is studied, and the unsteady flow adjusting process is displayed. The semi-implicit procedure of Ballhaus and Lomax (1974) is used to solve the small disturbance transonic potential equation. The physical aspects of the results, rather than the numerical details, are emphasized.

Ballhaus, W. F.↗
NASA NTRS1978

Some calculations of transonic potential flow for the NACA 64A006 airfoil with oscillating flap

A method for calculating the transonic flow over steady and oscillating airfoils was developed by Isogai. It solves the full potential equation with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. In this paper the method is described in general terms, and results are compared with experimental data for both steady flow and for oscillations at several values of reduced frequency. Good agreement for static pressures is shown for subcritical speeds, with increasing deviation as Mach number is increased into the supercritical speed range. Fair agreement with experiment was obtained at high reduced frequencies with larger deviations at low reduced frequencies.

Bennett, R. M.↗
NASA NTRS1979

An exploratory study of a finite difference method for calculating unsteady transonic potential flow

A method for calculating transonic flow over steady and oscillating airfoils was developed by Isogai. The full potential equation is solved with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. The method is described in general terms and results for the case of an airfoil with an oscillating flap are presented for Mach numbers 0.500 and 0.875. Although satisfactory results are obtained for some reduced frequencies, it is found that the numerical technique generates spurious oscillations in the indicial response functions and in the variation of the aerodynamic coefficients with reduced frequency. These oscillations are examined with a dynamic data reduction method to evaluate their effects and trends with reduced frequency and Mach number. Further development of the numerical method is needed to eliminate these oscillations.

Bennett, R. M.↗