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Results for “implicit method”

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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

An implicit marching procedure for the treatment of supersonic flow fields using the conservative full potential equation

A new aerodynamic prediction technique based on the conservative full potential equation is developed for the treatment of supersonic flow fields. This new technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar phi. The method produces results that compare well with Euler solvers and requires an order of magnitude less computer time and significantly less computer memory over existing nonlinear codes. The scalar phi formulation can be extended to handle subsonic pockets in the marching direction and also is suitable for developing inverse procedures where the shape corresponding to a prescribed loading is sought.

Shankar, V.↗
DOE OSTI2024

A fast, matrix-based method to perform omnidirectional pressure integration

Abstract Experimentally-measured pressure fields play an important role in understanding many fluid dynamics problems. Unfortunately, pressure fields are difficult to measure directly with non-invasive, spatially resolved diagnostics, and calculations of pressure from velocity have proven sensitive to error in the data. Omnidirectional line integration methods are usually more accurate and robust to these effects as compared to implicit Poisson equations, but have seen slower uptake due to the higher computational and memory costs, particularly in 3D domains. This paper demonstrates how omnidirectional line integration approaches can be converted to a matrix inversion problem. This novel formulation uses an iterative approach so that the boundary conditions are updated each step, preserving the convergence behavior of omnidirectional schemes while also keeping the computational efficiency of Poisson solvers. This method is implemented in Matlab and also as a GPU-accelerated code in CUDA-C++. The behavior of the new method is demonstrated on 2D and 3D synthetic and experimental data. Three-dimensional grid sizes of up to 125 million grid points are tractable with this method, opening exciting opportunities to perform volumetric pressure field estimation from 3D PIV measurements.

42 ENGINEERING↗
NASA NTRS1991

Generalized conjugate-gradient methods for the Navier-Stokes equations

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Ajmani, Kumud↗
NASA NTRS1986

On the boundary treatment in spectral methods for hyperbolic systems

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Canuto, C.↗
NASA NTRS1987

On the boundary treatment in spectral methods for hyperbolic systems

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Canuto, Claudio↗
NASA NTRS1993

Three-dimensional flow analysis inside turbomachinery stages with steady and unsteady Navier-Stokes method

This study presents a numerical method for solving the three-dimensional, Navier-Stokes equations for unsteady, viscous flow through multiple turbomachinery blade rows. The method solves the fully three-dimensional Navier-Stokes equations with an implicit scheme which is based on a control volume approach. A two-equation turbulence model with a low Reynolds number modification is employed in the present study. A third-order accurate upwinding scheme is used to approximate convection terms while a second order accurate central difference scheme is used for the discretization of viscous terms. A second-order accurate scheme is employed for the temporal discretization. The numerical method is applied to study the unsteady flow field of a subsonic turbine stage and the unsteady flow field inside a transonic, high-through-flow, axial compressor stage. The stage calculation is performed by coupling the stator and the rotor flow fields at each time step through an over-laid grid.

Copenhaver, W. W.↗
DOE OSTI2023

The Peridigm Meshfree Peridynamics Code

Abstract Peridigm is a meshfree peridynamics code written in C++ for use on large-scale parallel computers. It was originally developed at Sandia National Laboratories and is currently managed as an open-source, community driven software project. Its primary features include bond-based, state-based, and non-ordinary state-based constitutive models, bond failure laws, contact, and support for explicit and implicit time integration. To date, Peridigm has been used primarily by methods developers focused on solid mechanics and material failure. Peridigm utilizes foundational software components from Sandia’s Trilinos project and was designed for extensibility. This paper provides an overview of the solution methods implemented in Peridigm , a discussion of its software infrastructure, and demonstrates the use of Peridigm for the solution of several example problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Multiply Reduced Oligofluorenes: Their Nature and Pairing with THF-Solvated Sodium Ions

Conjugated oligofluorenes are chemically reduced up to five charges in tetrahydrofuran solvent and confirmed with clear spectroscopic evidence. Stimulated by these experimental results, we have conducted a comprehensive computational study of the electronic structure and the solvation structure of representative oligofluorene anions with a focus on the pairing between sodium ions and these multianions. In addition, using density functional theory (DFT) methods and a solvation model of both explicit solvent molecules and implicit polarizable continuum, we first elucidate the structure of tightly solvated free sodium ions, and then explore the pairing of sodium ions either in contact with reduced oligofluorenes or as solvent-separated ion pairs. Computed time-dependent-DFT absorption spectra are compared with experiments to assign the dominant ion pairing structure for each multianion. Computed ion pair binding energies further support our assignment. Lastly, the availability of different length and reducing level of oligofluorenes enables us to investigate the effects of total charge and charge density on the binding with sodium ions, and our results suggest both factors play important roles in ion pairing for small molecules. However, as the oligofluorene size grows, its charge density determines the binding strength with the sodium ion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Directing the far-from-equilibrium assembly of nanoparticles in confined liquid crystals by hydrodynamic fields

The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. Here, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark–Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Effects of surface charge and cluster size on the electrochemical dissolution of platinum nanoparticles using COMB3 and continuum electrolyte models

We study the site-dependent dissolution of platinum nanoparticles under electrochemical conditions to assess their thermodynamic stability as a function of shape and size using empirical molecular dynamics and electronic-structure models. The third-generation charge optimized many-body potential is employed to determine the validity of uniform spherical representations of the nanoparticles in predicting dissolution potentials (the Kelvin model). To understand the early stages of catalyst dissolution, implicit solvation techniques based on the self-consistent continuum solvation method are applied. It is demonstrated that interfacial charge and polarization can shift the dissolution energies by amounts on the order of 0.74 eV depending on the surface site and nanoparticle shape, leading to the unexpected preferential removal of platinum cations from highly coordinated sites in some cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Computational Studies of Solubilities of LiO 2 and Li 2 O 2 in Aprotic Solvents

Knowledge of the solubilities of Li 2 O 2 and LiO 2 in aprotic solvents is important for insight into the discharge and charge processes of Li-O 2 batteries, but these quantities are not well known. In this contribution, the solvation free energies of molecular LiO 2 and Li 2 O 2 in various organic solvents were calculated using various explicit and implicit solvent models, as well as ab initio molecular dynamics (AIMD) methods. Best estimates for the solvation energies from these calculations along with calculated lattice energies of Li 2 O 2 and LiO 2 were used to determine the solubility of bulk LiO 2 and Li 2 O 2 . The computed solubility of LiO 2 (1.8 × 10 -2 M) is about 15 orders higher than that of Li 2 O 2 (2.0 × 10 -17 M) due to a much less negative lattice energy of bulk LiO 2 compared to that of Li 2 O 2 . The difference in solubilities between LiO 2 and Li 2 O 2 likely will affect the nucleation and growth mechanisms and resulting morphologies of the products formed during battery discharge, influencing the performance of the battery cell. In conclusion, the calculated LiO 2 and Li 2 O 2 solubilities provide important information for fundamental studies of discharge and charge chemistries in Li-O 2 batteries.

25 ENERGY STORAGE↗
NASA NTRS1988

The age of the galactic disk

The galactic disk is a dissipative structure and must, therefore be younger than the halo if galaxy formation generally proceeds by collapse. Just how much younger the oldest stars in the galactic disk are than the oldest halo stars remains an open question. A fast collapse (on a time scale no longer than the rotation period of the extended protogalaxy) permits an age gap of the order of approximately 10 to the 9th power years. A slow collapse, governed by the cooling rate of the partially pressure supported falling gas that formed into what is now the thick stellar disk, permits a longer age gap, claimed by some to be as long as 6 Gyr. Early methods of age dating the oldest components of the disk contain implicit assumptions concerning the details of the age-metallicity relation for stars in the solar neighborhood. The discovery that this relation for open clusters outside the solar circle is different that in the solar neighborhood (Geisler 1987), complicates the earlier arguments. The oldest stars in the galactic disk are at least as old as NGC 188. The new data by Janes on NGC 6791, shown first at this conference, suggest a disk age of at least 12.5 Gyr, as do data near the main sequence termination point of metal rich, high proper motion stars of low orbital eccentricity. Hence, a case can still be made that the oldest part of the galactic thick disk is similar in age to the halo globular clusters, if their ages are the same as 47 Tuc.

Sandage, Allan↗
NASA NTRS1991

Simulation Of Flow In A Turbine Cascade

Report discusses application of lower-upper (LU) implicit numerical-integration scheme, together with interactive grid-generation method, to simulation of inviscid, compressible flow in two-dimensional model of turbine cascade. Study part of continuing effort to develop techniques for computation of complicated three-dimensional flows in turbomachinery.

Choo, Yung K.↗
NASA NTRS1990

Application of implicit numerical techniques to the solution of the three-dimensional diffusion equation

Implicit techniques for calculating three-dimensional, time-dependent heat diffusion in a cube are tested with emphasis on storage efficiency, accuracy, and speed of calculation. For this purpose, a tensor product technique with both Chebyshev collocation and finite differences and a generalized conjugate gradient technique with finite differences are used in conjunction with Crank-Nicolson discretization. An Euler explicit finite difference calculation is performed for use as a benchmark. The implicit techniques are found to be competitive with the Euler explicit method in terms of storage efficiency and speed of calculation and offer advantages both in accuracy and stability. Mesh stretching in the finite difference calculations is shown to markedly improve the accuracy of the solution.

Peltier, Leonard Joel↗
NASA NTRS1993

Further development towards a new virtual-pulse time integral methodology for general nonlinear transient thermal analysis

New developments describing the theoretical basis towards an effective virtual-pulse time integral procedure are presented for general nonlinear transient heat transfer problems. To validate the proposed methodology of computation, numerical test examples are given and comparisons are drawn with the implicit second-order accurate Crank-Nicolson technique. The proposed method shows superior or improved accuracy and stability characteristics for the models tested.

Tamma, K. K.↗
NASA NTRS2000

Parallel performance investigations of an unstructured mesh Navier-Stokes solver

A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.

Mavriplis, Dimitri J.↗
DOE OSTI2019

Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Implicit Kalman filtering

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Non-NASA Center↗