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Results for “implicit-explicit methods”

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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Overcoming Geometry-Induced Stiffness with IMplicit-Explicit (IMEX) Runge-Kutta Algorithms on Unstructured Grids with Applications to CEM, CFD, and CAA

My goal is to develop and implement efficient, accurate, and robust Implicit-Explicit Runge-Kutta (IMEX RK) methods [9] for overcoming geometry-induced stiffness with applications to computational electromagnetics (CEM), computational fluid dynamics (CFD) and computational aeroacoustics (CAA). IMEX algorithms solve the non-stiff portions of the domain using explicit methods, and isolate and solve the more expensive stiff portions using implicit methods. Current algorithms in CEM can only simulate purely harmonic (up to lOGHz plane wave) EM scattering by fighter aircraft, which are assumed to be pure metallic shells, and cannot handle the inclusion of coatings, penetration into and radiation out of the aircraft. Efficient MEX RK methods could potentially increase current CEM capabilities by 1-2 orders of magnitude, allowing scientists and engineers to attack more challenging and realistic problems.

Kanevsky, Alex↗
DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2025

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗
NASA NTRS1982

Mixed time integration methods for transient thermal analysis of structures

The computational methods used to predict and optimize the thermal structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a different yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Liu, W. K.↗
NASA NTRS1983

Mixed time integration methods for transient thermal analysis of structures

The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally-useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Liu, W. K.↗
NASA NTRS1982

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Adelman, H. M.↗
NASA NTRS1983

Improvement of mixed time implicit-explicit algorithms for thermal analysis of structures

Computer implementation aspects and numerical evaluation of the recently introduced mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally useful method of estimating the critical time step for a linear quadrilateral element is given herein for the methods introduced by Liu and co-workers. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Liu, W. K.↗
NASA NTRS1989

Finite element formulations for compressible flows

Researchers started their studies on the development and application of computational methods for compressible flows. Particular attention was given to proper numerical treatment of sharp layers occurring in such problems and to general mesh generation capabilities for intricate computational geometries. Mainly finite element methods enhanced with several state-of-the art techniques (such as the streamline-upwind/Petrov-Galerkin, discontinuity capturing, adaptive implicit-explicit, and trouped element-by-element approximate factorization schemes) were employed.

Tezduyar, Tayfun E.↗
DOE OSTI2024

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Combined AIE/EBE/GMRES approach to incompressible flows

Adaptive implicit-explicit (AIE), grouped element-by-element (GEBE), and generalized minimum residuals (GMRES) solution techniques for incompressible flows are combined. In this approach, the GEBE and GMRES iteration methods are employed to solve the equation systems resulting from the implicitly treated elements, and therefore no direct solution effort is involved. The benchmarking results demonstrate that this approach can substantially reduce the CPU time and memory requirements in large-scale flow problems. Although the description of the concepts and the numerical demonstration are based on the incompressible flows, the approach presented here is applicable to larger class of problems in computational mechanics.

Liou, J.↗
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 OSTI2024

Improving ADAM through an implicit-explicit (IMEX) time-stepping approach

The ADAM optimizer, often used in machine learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. Here, this work shows that the classical ADAM algorithm is a first-order implicit-explicit (IMEX) Euler discretization of the underlying ODE. Employing the time discretization point of view, we propose new extensions of the ADAM scheme obtained by using higher-order IMEX methods to solve the ODE. Based on this approach, we derive a new optimization algorithm for neural network training that performs better than classical ADAM on several regression and classification problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

A numerical classical flutter analysis of advanced propellers

A three-dimensional Euler solver is coupled with a three-dimensional structural dynamics model to investigate flutter of propfans. An implicit-explicit hybrid scheme is used to reduce computational time for the solution of Euler equations. The aeroelastic equations are formulated in normal modes and are solved for flutter in frequency domain. The required generalized forces are obtained using a pulse response method. Computations show that the instability is dominated by the second mode frequency as was observed in experiment.

Srivastava, R.↗
DOE OSTI2024

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Development of an implicit electromagnetic capability for a hybrid gyrokinetic ion-fluid electron model

Here we report on the development and implementation of a hybrid kinetic ion–fluid electron model for electromagnetic COGENT simulations of edge plasmas. COGENT is a finite-volume gyrokinetic code that employs a locally field-aligned coordinate system combined with a mapped multi-block grid technology to handle strongly anisotropic edge plasma turbulence. The simulation model involves the long-wavelength limit of the ion gyrokinetic equation coupled to the vorticity and Ohm's law equations for the electromagnetic field perturbations. In order to handle the fast Alfvén wave time scales, an implicit-explicit time integration approach with a physics-based preconditioner is used. The model is successfully applied to the simulations of ion-scale resistive-drift ballooning turbulence in a toroidal annulus geometry. Substantial speed-up over a fully explicit time integration approach is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2025

Electromagnetic Transient Simulation of Photovoltaic Inverter Using Implicit-Explicit Solver

This paper introduces the implementation of electromagnetic transient (EMT) simulations of a photovoltaic (PV) inverter module using the Implicit-Explicit (ImEx) solver in the Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS). This study demonstrates the effectiveness of the ImEx solver in overcoming the challenges inherent in simulating the complex dynamics of PV inverter modules. Furthermore, using SUNDIALS’ ImEx solver module ARKODE for EMT simulation automates key aspects of the process, such as numerical integration, providing substantial benefits including enhanced consistency, faster implementation, reduced human error, and the capability to handle the complexities of advanced numerical integration. By conducting comparative simulations with an implicit method used in commercial software, the research showcases the ImEx solver’s capability in achieving high accuracy and reliability. Results indicate that leveraging the ImEx approach significantly enhances modeling fidelity and reduces simulation setup times, offering a promising tool for the EMT analysis of PV inverter systems in power electronics-dominated power grids.

Choi, Jongchan [ORNL] (ORCID:000000025952455X)↗
NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗