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Results for “explicit and implicit 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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

ADI on staggered mesh - A method for the calculation of compressible convection

An alternating direction implicit (ADI) method has been applied to a staggered grid for the computation of convection in a highly stratified fluid. Since artificial viscosity is not needed, subtle effects like the onset of convection can be studied. These computations compare well with the 2-D results by Graham (1975) and also agree with standard Boussinesq results when taken to that limit. Good efficiency has been achieved with a time step hundreds of times larger than the stability limit imposed by the explicit treatment of diffusion and the Courant number is not restricted to be below 1. The Navier-Stokes equation contains cross spatial derivatives which are treated explicitly in most ADI schemes. The destabilizing effect of such a practice on a 2-D model system with second-order spatial derivative terms only was analyzed and found to be not excessive.

Chan, K. L.↗
NASA NTRS1990

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗
NASA NTRS1995

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Scott, James R.↗
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 NTRS1977

Study of effects of injector geometry on fuel-air mixing and combustion

An implicit finite-difference method has been developed for computing the flow in the near field of a fuel injector as part of a broader study of the effects of fuel injector geometry on fuel-air mixing and combustion. Detailed numerical results have been obtained for cases of laminar and turbulent flow without base injection, corresponding to the supersonic base flow problem. These numerical results indicated that the method is stable and convergent, and that significant savings in computer time can be achieved, compared with explicit methods.

Bangert, L. H.↗
NASA NTRS1986

Higher-order flux difference splitting schemes for the Euler equations using upstream interpolations

A class of explicit two time-level, 2p + 1 space-point, (2p 1)-th order, upwind-biased flux difference splitting schemes are proposed for the numerical advection based on Lagrange's interpolation, and the method is an accord with the physical domain of dependence. A normalized Jacobian coefficient matrix is introduced to convert the schemes to hyperbolic systems of conservation laws, and approaches to make the higher-order schemes total variation stable are discussed. Accuracy and stability of the present schemes are examined, and implicit total variation diminishing schemes are developed for steady-state calculations.Application to gasdynamic problems for both steady and unsteady flows covering a wide range of Mach numbers is considered, and results for a blast wave passing a cylinder, and head-on collision of two blast waves over a circular arc, are presented. The flow patterns were found to be symmetric, and good resolution of flow structures was obtained.

Yang, J. Y.↗
NASA NTRS1991

An implicit method for the nonlinear modelling and simulation of piezoceramic actuators displaying hysteresis

Experiments have shown that piezoceramic materials display a nonlinear relationship between the applied electric field and the actuation strain. This relationship also displays a substantial hysteresis upon reversal of the applied field. In this paper, piezoceramic actuator models are incorporated into the structural equations of motion to arrive at a set of nonlinear actively controlled structural equations of motion. A new implicit algorithm for determining the time history of the actively controlled structure is presented. The algorithm employs the trapezoidal rule for stepping the equations forward in time. The algorithm is compared to an explicit algorithm and is shown to provide greater numerical accuracy. In addition, the numerical stability and convergence characteristics are presented via example. The new algorithm displays convergence and stability properties that are comparable to the standard trapezoidal rule used for dynamic systems without hysteresis.

Leigh, Timothy D.↗
NASA NTRS1993

A solution-adaptive hybrid-grid method for the unsteady analysis of turbomachinery

A solution-adaptive method for the time-accurate analysis of two-dimensional flows in turbomachinery is described. The method employs a hybrid structured-unstructured zonal grid topology in conjunction with appropriate modeling equations and solution techniques in each zone. The viscous flow region in the immediate vicinity of the airfoils is resolved on structured O-type grids while the rest of the domain is discretized using an unstructured mesh of triangular cells. Implicit, third-order accurate, upwind solutions of the Navier-Stokes equations are obtained in the inner regions. In the outer regions, the Euler equations are solved using an explicit upwind scheme that incorporates a second-order reconstruction procedure. An efficient and robust grid adaptation strategy, including both grid refinement and coarsening capabilities, is developed for the unstructured grid regions. Grid adaptation is also employed to facilitate information transfer at the interfaces between unstructured grids in relative motion. Results for grid adaptation to various features pertinent to turbomachinery flows are presented. Good comparisons between the present results and experimental measurements and earlier structured-grid results are obtained.

Mathur, Sanjay R.↗
NASA NTRS2016

Overview of the NASA Glenn Flux Reconstruction Based High-Order Unstructured Grid Code

A computational fluid dynamics code based on the flux reconstruction (FR) method is currently being developed at NASA Glenn Research Center to ultimately provide a large- eddy simulation capability that is both accurate and efficient for complex aeropropulsion flows. The FR approach offers a simple and efficient method that is easy to implement and accurate to an arbitrary order on common grid cell geometries. The governing compressible Navier-Stokes equations are discretized in time using various explicit Runge-Kutta schemes, with the default being the 3-stage/3rd-order strong stability preserving scheme. The code is written in modern Fortran (i.e., Fortran 2008) and parallelization is attained through MPI for execution on distributed-memory high-performance computing systems. An h- refinement study of the isentropic Euler vortex problem is able to empirically demonstrate the capability of the FR method to achieve super-accuracy for inviscid flows. Additionally, the code is applied to the Taylor-Green vortex problem, performing numerous implicit large-eddy simulations across a range of grid resolutions and solution orders. The solution found by a pseudo-spectral code is commonly used as a reference solution to this problem, and the FR code is able to reproduce this solution using approximately the same grid resolution. Finally, an examination of the code's performance demonstrates good parallel scaling, as well as an implementation of the FR method with a computational cost/degree- of-freedom/time-step that is essentially independent of the solution order of accuracy for structured geometries.

High-Order Methods↗
NASA NTRS1994

Unstructured grid methods for the simulation of 3D transient flows

A description of the research work undertaken under NASA Research Grant NAGW-2962 has been given. Basic algorithmic development work, undertaken for the simulation of steady three dimensional inviscid flow, has been used as the basis for the construction of a procedure for the simulation of truly transient flows in three dimensions. To produce a viable procedure for implementation on the current generation of computers, moving boundary components are simulated by fixed boundaries plus a suitably modified boundary condition. Computational efficiency is increased by the use of an implicit time stepping scheme in which the equation system is solved by explicit multistage time stepping with multigrid acceleration. The viability of the proposed approach has been demonstrated by considering the application of the procedure to simulation of a transonic flow over an oscillating ONERA M6 wing.

Morgan, K.↗
DOE OSTI2026

Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials

Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry optimization. While these geometries do not consistently reach DFT-level chemical accuracy or convergence, they can still improve downstream performance compared to non-relaxed structures. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molecular geometries that benefit property predictions. Our code is publicly available at: https://github.com/divelab/AIRS/.

Fu, Cong [Texas A & M Univ., College Station, TX (↗
NASA NTRS1998

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Koppenhoefer, Kyle C.↗
NASA NTRS1995

A computational fluid dynamics simulation of the hypersonic flight of the Pegasus(TM) vehicle using an artificial viscosity model and a nonlinear filtering method

The computational fluid dynamics code, PARC3D, is tested to see if its use of non-physical artificial dissipation affects the accuracy of its results. This is accomplished by simulating a shock-laminar boundary layer interaction and several hypersonic flight conditions of the Pegasus(TM) launch vehicle using full artificial dissipation, low artificial dissipation, and the Engquist filter. Before the filter is applied to the PARC3D code, it is validated in one-dimensional and two-dimensional form in a MacCormack scheme against the Riemann and convergent duct problem. For this explicit scheme, the filter shows great improvements in accuracy and computational time as opposed to the nonfiltered solutions. However, for the implicit PARC3D code it is found that the best estimate of the Pegasus experimental heat fluxes and surface pressures is the simulation utilizing low artificial dissipation and no filter. The filter does improve accuracy over the artificially dissipative case but at a computational expense greater than that achieved by the low artificial dissipation case which has no computational time penalty and shows better results. For the shock-boundary layer simulation, the filter does well in terms of accuracy for a strong impingement shock but not as well for weaker shock strengths. Furthermore, for the latter problem the filter reduces the required computational time to convergence by 18.7 percent.

Mendoza, John Cadiz↗
NASA NTRS2000

Application of Soft Computing in Coherent Communications Phase Synchronization

The use of soft computing techniques in coherent communications phase synchronization provides an alternative to analytical or hard computing methods. This paper discusses a novel use of Adaptive Neuro-Fuzzy Inference Systems (ANFIS) for phase synchronization in coherent communications systems utilizing Multiple Phase Shift Keying (MPSK) modulation. A brief overview of the M-PSK digital communications bandpass modulation technique is presented and it's requisite need for phase synchronization is discussed. We briefly describe the hybrid platform developed by Jang that incorporates fuzzy/neural structures namely the, Adaptive Neuro-Fuzzy Interference Systems (ANFIS). We then discuss application of ANFIS to phase estimation for M-PSK. The modeling of both explicit, and implicit phase estimation schemes for M-PSK symbols with unknown structure are discussed. Performance results from simulation of the above scheme is presented.

Drake, Jeffrey T.↗
DOE OSTI2025

Liquid Phase Modeling in Porous Media: Adsorption of Methanol and Ethanol in H-MFI in Condensed Water

Zeolites are used in the chemical and separation industries for their exceptional selectivity, adsorption capacity, regenerability, and stability in gas and liquid phase processing. Here, we developed an explicit solvation method for predicting solvent/condensed phase effects on adsorption free energies in microporous media such as zeolites based on the hybrid quantum mechanical/molecular mechanical free energy perturbation (QM/MM-FEP) technique. Our explicit solvation method for zeolite systems, called eSZS, aims to capture site-specific interactions during the adsorption process at the Brønsted acid sites of H-MFI zeolite while still considering the diverse configuration space of the solvent molecules. This strategy is ideal for chemical reactions or adsorbates that interact with the microporous medium in few distinct adsorbate/transition state configurations, i.e., the harmonic or similar approximations are acceptable for the adsorbate/transition state while such approximations break down for the solvent molecules that require extensive configuration space sampling. In this way, our approach effectively overcomes the limitations of implicit solvation models and classical force field methods for describing solvation effects on chemical reactions within porous materials such as zeolites. Specifically, in this study, we investigated various aspects of our hybrid QM/MM approach, including QM cluster size dependencies in a periodic electrostatically embedded cluster model (PEECM), rules for link atoms at the QM/MM boundary, and functional and basis set considerations for converged and reasonably accurate gas and aqueous phase methanol and ethanol adsorption free energy predictions in H-MFI. For gas phase adsorption of methanol and ethanol in H-MFI at a Brønsted acid site in T12 position, we compute adsorption free energies at 298 K of −0.61 and −0.75 eV, respectively, using a PEECM containing 50 Si and 1 Al atom with ωB97x-D/def2-TZVP level of theory. For solvent effect calculations, we sample the aqueous phase using grand canonical Monte Carlo (GCMC) simulations to (1) obtain a mean field of electrostatic interactions in the reaction system and (2) perform a rigorous free energy perturbation calculation. Similar to the experimentally and computationally observed endergonic solvation effects observed for hydrocarbon adsorption on metal surfaces, we also observe that a condensed aqueous environment destabilizes methanol and ethanol at these acid sites in H-MFI at 298 K. Specifically, the computed solvation free energies of adsorption (ΔΔG solv ) for methanol and ethanol are +0.44 and +0.54 eV, respectively. From this study, it is evident that adsorbates (methanol and ethanol) are competing with water for adsorption space inside the H-MFI zeolite, leading to an endergonic solvation effect. Here, we expect that the endergonic, aqueous solvent effect during adsorption in microporous zeolites is highly tunable by changing the pore size and hydrophobicity of the microporous material as this will affect the water density inside the pore structure.

Adsorption↗
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 OSTI2026

INR-TEM: Robust cavity detection in multifocus TEM images via implicit neural representations

When characterizing materials using transmission electron microscopy (TEM) images, detecting and quantifying small features in microstructures, such as cavities, pose significant challenges. Off-the-shelf object detection models, including YOLOv8, show considerable performance degradation, particularly when images vary in resolution and the objects of interest possess a low percentage of the total image region of interest. In this study, we introduce a novel detection pipeline that incorporates an implicit neural representation (INR)-based detection method, INR-TEM, and two-modality imaging (e.g., under-focused and over-focused images typically acquired during materials characterization) to improve object detection performance. The INR-TEM method incorporates a pixel-wise prediction principle inspired by pixel-wise centerness weighting. INR-TEM demonstrates superior robustness to resolution variability, maintaining high detection accuracy even at low image resolutions compared to YOLOv8. To leverage INR-TEM effectively in real-world two-modality characterization applications, we further integrate a two-stage motion correction pipeline designed explicitly for aligning multifocus TEM images. The alignment process, comprising keypoint (based on scale-invariant feature transform, SIFT) and intensity matching, significantly mitigates the adverse effects of perceived motion-induced image degradation during through-focal TEM imaging, directly enhancing INR-TEM’s detection capability over conventional single-focus images. Our integrated INR-TEM cavity detection framework notably improves performance across various cavity sizes, outperforming off-the-shelf YOLOv8 detections that rely on a single image modality.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1978

Numerical solution of two-dimensional turbulent blunt body flows with an impinging shock

An implicit finite-difference method has been developed to compute two-dimensional, turbulent, blunt body flows with an impinging shock wave. The full time-averaged Navier-Stokes equations are solved with algebraic eddy viscosity and turbulent Prandtl number models employed for shear stress and heat flux. The irregular-shaped bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied. A Type III turbulent shock interference flow field has been computed and the numerical results compare favorably with existing experimental data. In addition, comparisons are made between the present implicit code and a previous explicit code.

Tannehill, J. C.↗