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Results for “explicit solution”

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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

An investigation of cell centered and cell vertex multigrid schemes for the Navier-Stokes equations

Two efficient and robust finite-volume multigrid schemes for solving the Navier-Stokes equations are investigated. These schemes employ either a cell centered or a cell vertex discretization technique. An explicit Runge-Kutta algorithm is used to advance the solution in time. Acceleration techniques are applied to obtain faster steady-state convergence. Accuracy and convergence of the schemes are examined. Computational results for transonic airfoil flows are essentially the same, even for a coarse mesh. Both schemes exhibit good convergence rates for a broad range of artificial dissipation coefficients.

Radespiel, R.↗
NASA NTRS1988

Adaptive implicit-explicit finite element algorithms for fluid mechanics problems

The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.

Tezduyar, T. E.↗
NASA NTRS1990

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.

Michelassi, V.↗
NASA NTRS1991

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Michelassi, V.↗
NASA NTRS1994

Simultaneous soft and hard X-ray spectroscopy of AM Herculis with EXOSAT: Discovery of photospheric absorption features

We present 0.1-10 keV spectroscopic observations of AM Herculis obtained with the Transmission Grating Spectrometers and Medium Energy experiments on EXOSAT, taken when the object was in its 'reversed X-ray mode.' The observation covers over six binary orbits without interruption, enabling us to analyze the phase and intensity dependence of both the hard and the soft spectrum simultaneously. We resolve the optically thick soft X-ray spectrum, and find definite evidence for time- and phase-dependent photospheric absorption structure arising in the white dwarf atmosphere. We present a simple empirical analysis of the combined soft and hard X-ray spectra, to examine whether the effect of a better determination of the column density of neutral absorbing material, afforded by our data, would solve the problem of the large relative soft X-ray overluminosity previously observed in AM Her. We find that a single absorbing column fits the entire spectrum, and that the column densities implied are indeed substantially lower than previously estimated. However, during half the binary orbit we still determine a strong lower limit to the soft-to-hard luminosity ratio of L(sub soft)/L(sub hard) is greater than or approximately equal to 10, in conflict with the simple radiative shock models for the accretion region. We argue that this indicates the need to reexamine the luminosity problem using explicit models for the emission spectrum based on a full solution of the atmospheric radiative transfer problem.

Paerels, Frits↗
NASA NTRS2019

Numerical analysis of unsteady flow in a converging-diverging nozzle

This study investigates the physics of jet noise by the numerical solution of the three dimensional unsteady Navier-Stokes equations for a low-supersonic jet (Mach numbers on the order of 1.4) from a converging-diverging (C-D) nozzle and mixing with a subsonic surrounding flow. The numerical method used for the solution of these equations is the second order accurate MacCormack explicit predictor-corrector scheme. The numerical results are compared to the experimental results of Yamamoto for the same C-D nozzle geometry and similar operating conditions. The goal of the study is to use numerical simulation techniques to resolve accurately physical processes which contribute to jet noise, and to assess whether performing these simulations in a three dimensional geometry is worth the additional cost in computing resources as compared to a comparable simulation on a two dimensional planar or axisymmetric geometry. Scientific visualization is used to observe the spreading characteristics of the jet, as well as to examine the structure of the shocks within the jet core. The time average velocity and turbulence intensity level at various locations are computed and compared with experimental results. A two point space-time cross correlation is used to compute the mean convection speed through the shear layer, and these predictions are compared with results from theory.

James N Scott↗
NASA NTRS2002

Cirrus Parcel Model Comparison Phase 2

The Cirrus Parcel Model Comparison (CPMC) project, a project of the GEWEX Cloud System Study Working Group on cirrus clouds (GCSS WG2), is an international effort to advance our knowledge of numerical simulations of cirrus cloud initiation. This project was done in two phases. In Phase 1 of CPMC, the critical components determining the predicted cloud microphysical properties were identified using parcel models in which the aerosol and ice crystal size distributions are explicitly resolved, the formulation of the homogeneous freezing of aqueous solution droplets, especially the gradient of nucleation rate with respect to solution concentration; aerosol growth modeling; and the mass accommodation coefficient of water vapor on ice surface (the deposition coefficient). In Phase 1, all simulations were conducted using a given background aerosol distribution. To complete the comparison study, participant model responses to a range of background aerosol distributions are investigated in Phase 2.

Lin, Ruei-Fong↗
NASA NTRS2011

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Fisher, Travis C.↗
DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
NASA NTRS1982

An analytic approach to two-fixed-impulse transfers between Keplerian orbits

Solutions are obtained for the two-impulse transfer of a vehicle between arbitrary inclined orbits in an inverse-square force field with the restriction that the magnitude of each of the two impulses has a fixed preassigned value. The two magnitudes need not be equal. The equations for the conservation of angular momentum and energy are augmented by the Laplace integral; these equations establish linear relationships between several of the variables. This set of linear equations and one of two quadratic equations constitute the analytically tractable part of the solution. The remaining part, consisting of finding the zeros (if they exist) of a single trigonometric function of one variable, is solved using numerical methods. Explicit lower bounds on each of the magnitudes of the two impulses are obtained by requiring the solution be real. Graphical results are presented to illustrate the solution.

Jezewski, D. J.↗
NASA NTRS1991

Engineering calculations of three-dimensional inviscid hypersonic flow fields

An approximate solution technique has been developed for three-dimensional, inviscid, hypersonic flows. The method uses Maslen's explicit pressure equation and the assumption of approximate stream surfaces in the shock layer. This approximation represents a simplification of Maslen's asymmetric method. The solution procedure involves iteratively changing the shock shape in the subsonic-transonic region until the correct body shape is obtained. Beyond this region, the shock surface is determined by using a marching procedure. Results are presented herein for a paraboloid and elliptic cone at angle of attack. Calculated surface pressure distributions, shock shapes, and property profiles are compared with experimental data and finite-difference solutions of the Euler equations. Comparisons of the results of the present method with experimental data and detailed predictions are very good. Since the present method provides a very rapid computational procedure, it can be used for parametric or preliminary design applications. One useful application would be to incorporate a heating procedure for aerothermal studies.

Riley, Christopher J.↗
NASA NTRS1995

Separation of crack extension modes in orthotropic delamination models

In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict composite delamination. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode 1 and mode 2 energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, Delta. In this work, a method is presented for using the VCCT to extract Delta-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, Delta-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-tip fields is used to determine the explicit Delta dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Delta. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Delta-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The Delta-independent modes extracted using this technique can also serve as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Beuth, Jack L.↗
NASA NTRS1993

Distributed parallel processing applied to an implicit multigrid Euler/Navier-Stokes algorithm

An implicit multigrid algorithm for the solution of the Euler and Navier-Stokes equations has been implemented within the framework of multiple block-structured grids in which the physical domain is spatially decomposed into several blocks and the solution is advanced in parallel on each block. Utilities have been developed to implement such a scheme in a distributed computing environment. The multi-block algorithm is designed so that the explicit residual calculation is identical to that of single-block scheme, and therefore converged solutions for both schemes must be the same. To accelerate convergence, synchronous and asynchronous multigrid strategies are implemented. Significant speedups have been achieved in a multiple processor environment, while convergence rates similar to those of the single-block scheme are observed.

Tysinger, T. L.↗
NASA NTRS1997

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure.

Deavours, Daniel D.↗
NASA NTRS2019

WRLES: Wave Resolving Large-Eddy Simulation Code, Theory and Usage

A computational fluid dynamics code has been developed for large-eddy simulations (LES) of turbulent flow. The code uses high-order of accuracy and high-resolution numerical methods to minimize solution error and maximize the resolution of the turbulent structures. Spatial discretization is performed using explicit central differencing. The central differencing schemes in the code include 2nd- to 12th-order standard central difference methods as well as 7-, 9-, 11- and 13-point dispersion relation preserving schemes. Solution filtering and high-order shock capturing are included for stability. Time discretization is performed using multistage Runge-Kutta methods that are up to 4th order accurate. Several options are available to model turbulence including: Baldwin-Lomax and Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence models, and Smagorinsky, Dynamic Smagorinsky and Vreman sub-grid scale models for LES. This report presents the theory behind the numerical and physical models used in the code and provides a user's manual to the operation of the code.

High-Order↗
NASA NTRS1993

Nonlinear vortex trail dynamics. II - Analytic solutions

Spatially periodic large amplitude solutions of the von Karman model are obtained in the neighborhood of singularities. These singularities correspond to vortex clusters in the physical plane. The quasi-periodic and unbounded solutions found analytically confirm earlier numerical work and show qualitative agreement with experimental observations of large-scale phenomena of vortex trails. Separatrices or heteroclinic orbits were explicitly found for an integrable approximate equation, which indicate that the von Karman model itself supports chaotic solutions.

Lim, Chjan C.↗
DOE OSTI2023

An Efficient Reactive Force Field without Explicit Coordination Dependence for Studying Caustic Aluminum Chemistry

Reactive force fields (RFFs) are an expedient approach to sample chemical reaction paths in complex systems, relative to density functional theory. However, there is continued need to improve efficiencies, specifically in systems that have slow transverse degrees of freedom, as in highly viscous and superconcentrated solutions. Here, we present an RFF that is differentiated from current models (e.g., ReaxFF) by omitting explicit dependence on the atom coordination and employing a small parameter set based on Lennard-Jones, Gaussian, and Stillinger–Weber potentials. In this study, the model was parametrized from AIMD simulation data and is used to model aluminate reactivity in sodium hydroxide solutions with extensive validation against experimental radial distribution functions, computed free energy profiles for oligomerization, and formation energies. In conclusion, the model enables simulation of early stage Al(OH) 3 nucleation which has significant relevance to industrial processing of aluminum and has a computational cost that is reduced by 1 order of magnitude relative to ReaxFF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗