Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergence analysis”

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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Diffusion Synthetic Acceleration for High-Order Discontinuous Finite Element SN Transport Schemes and Application to Locally Refined Unstructured Meshes

Diffusion synthetic acceleration (DSA) schemes compatible with adaptive mesh refinement (AMR) grids are derived for the SN transport equations discretized using high-order discontinuous finite elements. These schemes are directly obtained from the discretized transport equations by assuming a linear dependence in angle of the angular flux along with an exact Fick's law and, therefore, are categorized as partially consistent. These schemes are akin to the symmetric interior penalty technique applied to elliptic problems and are all based on a second-order discontinuous finite element discretization of a diffusion equation (as opposed to a mixed or P1 formulation). Therefore, they only have the scalar flux as unknowns. A Fourier analysis has been carried out to determine the convergence properties of the three proposed DSA schemes for various cell optical thicknesses and aspect ratios. Out of the three DSA schemes derived, the modified interior penalty (MIP) scheme is stable and effective for realistic problems, even with distorted elements, but loses effectiveness for some highly heterogeneous configurations. The MIP scheme is also symmetric positive definite and can be solved efficiently with a preconditioned conjugate gradient method. Its implementation in an AMR SN transport code has been performed for both source iteration and GMRes-based transport solves, with polynomial orders up to 4. Numerical results are provided and show good agreement with the Fourier analysis results. Results on AMR grids demonstrate that the cost of DSA can be kept low on locally refined meshes.

42 ENGINEERING↗
NASA NTRS1996

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

Reddy, T. S. R.↗
DOE OSTI2016

Proof-of-Concept Study for Uncertainty Quantification and Sensitivity Analysis using the BRL Shaped-Charge Example

These are the slides for a graduate presentation at Mississippi State University. It covers the following: the BRL Shaped-Charge Geometry in PAGOSA, mesh refinement study, surrogate modeling using a radial basis function network (RBFN), ruling out parameters using sensitivity analysis (equation of state study), uncertainty quantification (UQ) methodology, and sensitivity analysis (SA) methodology. In summary, a mesh convergence study was used to ensure that solutions were numerically stable by comparing PDV data between simulations. A Design of Experiments (DOE) method was used to reduce the simulation space to study the effects of the Jones-Wilkins-Lee (JWL) Parameters for the Composition B main charge. Uncertainty was quantified by computing the 95% data range about the median of simulation output using a brute force Monte Carlo (MC) random sampling method. Parameter sensitivities were quantified using the Fourier Amplitude Sensitivity Test (FAST) spectral analysis method where it was determined that detonation velocity, initial density, C1, and B1 controlled jet tip velocity.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1987

Input error versus output error model reference adaptive control

Algorithms for model reference adaptive control were developed in recent years, and their stability and convergence properties have been investigated. Typical algorithms in continuous time involve strictly positive real conditions on the reference model, while similar discrete time algorithms do not require such conditions. It is shown how algorithms differ by the use of an input error versus an output error, and present a continuous time input error adaptive control algorithm which does not involve SPR conditions. The connections with other schemes are discussed. The input error scheme has general stability and ocnvergence properties that are similar to the output error scheme. However, analysis using averaging methods reveals some preferable convergence properties of the input error scheme. Several other advantages are also discussed.

Bodson, Marc↗
NASA NTRS2000

Discharge Coefficients for Axisymmetric Supersonic Nozzles

Computational Fluid Dynamics (CFD) analysis was used to compute effective nozzle discharge coefficients for subscale sharp-edged converging/diverging nozzles, with a variety of convergence half-angles, motor operating conditions, and two propellants with different ballistics. Convergence half-angles ranged from 0 to 80 deg. Analysis was conducted at total temperatures from 2946K (5303R) to 3346K (6023R) and over total pressures ranged from 2.72 MPa (395 psia) to 20.68 MPa (3000 psia). Area ratios (A(sub e)/A*) ranged from 7.43 to 9.39. Ratio of specific heats (gamma) ranged from 1.13 to 1.18. Throat and exit Reynolds numbers were calculated to be 8.26 x 10(exp 5) and 5.51 x 10(exp 5), respectively. Present results of nozzle discharge coefficients are reported and correlated as a function of nozzle convergence half-angle (theta(sub c)) and area ratios (A(sub e)/A*) for a constant divergence half-angle (theta(sub d)) of 15 deg. Computed discharge coefficients ranged from 0.88 to 0.97. They are compared with theory and experimental data available in literature. Available turbulence models with respect to grid refinements and heat transfer are discussed.

Ahmad, Rashid A.↗
NASA NTRS1988

A global-local finite element method suitable for parallel computations

A global-local finite element analysis procedure is developed based on the fast convergent nature of FEM in displacement. A special scheme is used to utilize the global displacement solution as boundary conditions for local regions of interest. In the local region, a refined mesh is used for further stress analysis. This global-local procedure can be easily programmed in parallel on MIMD multi-processor computers for significant time savings. A Sequent Balance 21000 system is used for demonstrating the parallel programming.

Sun, C. T.↗
DOE OSTI2021

Simultaneous compression and opacity data from time-series radiography with a Lagrangian marker

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. Additionally, if the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Extended forward sensitivity analysis of one-dimensional isothermal flow

Sensitivity analysis and uncertainty quantification is an important part of nuclear safety analysis. In this work, forward sensitivity analysis is used to compute solution sensitivities on 1-D fluid flow equations typical of those found in system level codes. Time step sensitivity analysis is included as a method for determining the accumulated error from time discretization. The ability to quantify numerical error arising from the time discretization is a unique and important feature of this method. By knowing the relative sensitivity of time step with other physical parameters, the simulation is allowed to run at optimized time steps without affecting the confidence of the physical parameter sensitivity results. The time step forward sensitivity analysis method can also replace the traditional time step convergence studies that are a key part of code verification with much less computational cost. One well-defined benchmark problem with manufactured solutions is utilized to verify the method; another test isothermal flow problem is used to demonstrate the extended forward sensitivity analysis process. Through these sample problems, the paper shows the feasibility and potential of using the forward sensitivity analysis method to quantify uncertainty in input parameters and time step size for a 1-D system-level thermal-hydraulic safety code. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Energy Systems Integration: A Convergence of Ideas

Energy systems integration (ESI) enables the effective analysis, design, and control of these interactions and interdependencies along technical, economic, regulatory, and social dimensions. By focusing on the optimization of energy from all systems, across all pathways, and at all scales, we can better understand and make use of the co-benefits that result to increase reliability andperformance, reduce cost, and minimize environmental impacts. This white paper discusses systems integration and the research in new control architectures that are optimized at smaller scales but can be aggregated to optimize energy systems at any scale and would allow replicable energy solutions across boundaries of existing and new energy pathways.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals

We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.

coupled cluster theory↗
NASA NTRS1993

On the stability analysis of approximate factorization methods for 3D Euler and Navier-Stokes equations

The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.

Demuren, A. O.↗
DOE OSTI2020

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation

Here, we study reproducing kernel (RK) collocation method for peridynamic Navier equation. In the first part, we apply a linear RK approximation to both displacement and dilatation, and then back-substitute dilatation and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit for a fixed nonlocal interaction length and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. In the second part, we apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lamé parameters satisfy λ ≥ μ to avoid extra assumptions on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.

42 ENGINEERING↗
NASA NTRS1994

Prediction of contact path and load sharing in spiral bevel gears

A procedure is presented to perform a contact analysis of spiral bevel gears in order to predict the contact path and the load sharing as the gears roll through mesh. The approach utilizes recent advances in automated contact methods for nonlinear finite element analysis. A sector of the pinion and gear is modeled consisting of three pinion teeth and four gear teeth in mesh. Calculation of the contact force and stresses through the gear meshing cycle are demonstrated. Summary of the results are presented using three dimensional plots and tables. Issues relating to solution convergence and requirements for running large finite element analysis on a supercomputer are discussed.

Bibel, George D.↗
NASA NTRS2006

Arbitrary Steady-State Solutions with the K-epsilon Model

Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.

Rumsey, Christopher L.↗
DOE OSTI2017

Geometry and growth contributions to cosmic shear observables

We explore the sensitivity of weak-lensing observables to the expansion history of the Universe and to the growth of cosmic structures, as well as the relative contribution of both effects to constraining cosmological parameters. We utilize ray-tracing dark-matter-only N-body simulations and validate our technique by comparing our results for the convergence power spectrum with analytic results from past studies. We then extend our analysis to non-Gaussian observables which cannot be easily treated analytically. We study the convergence (equilateral) bispectrum and two topological observables, lensing peaks and Minkowski functionals, focusing on their sensitivity to the matter density Ω m and the dark energy equation of state w. We find that a cancellation between the geometry and growth effects is a common feature for all observables and exists at the map level. It weakens the overall sensitivity by factors of up to 3 and 1.5 for w and Ω m , respectively, with the bispectrum worst affected. However, combining geometry and growth information alleviates the degeneracy between Ω m and w from either effect alone. As a result, the magnitudes of marginalized errors remain similar to those obtained from growth-only effects, but with the correlation between the two parameters switching sign. Furthermore, these results shed light on the origin of the cosmology sensitivity of non-Gaussian statistics and should be useful in optimizing combinations of observables.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

On LPMHSS-based iteration methods for a class of weakly nonlinear systems

In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Unraveling Local Structure of Molten Salts via X-ray Scattering, Raman Spectroscopy, and Ab Initio Molecular Dynamics

In this work, we resolve a long-standing issue concerning the local structure of molten MgCl 2 by employing a multimodal approach, including X-ray scattering and Raman spectroscopy, along with the theoretical modeling of the experimental spectra based on ab initio molecular dynamics (AIMD) simulations utilizing several density functional theory (DFT) methods. We demonstrate the reliability of AIMD simulations in achieving excellent agreement between the experimental and simulated spectra for MgCl 2 and 50 mol % MgCl 2 + 50 mol % KCl, and ZnCl 2 , thus allowing structural insights not directly available from experiment alone. A thorough computational analysis using five DFT methods provides a convergent view that octahedrally coordinated magnesium in pure MgCl 2 upon melting preferentially coordinates with five chloride anions to form distorted square pyramidal polyhedra that are connected via corners and to a lesser degree via edges. This is contrasted with the results for ZnCl 2 , which does not change its tetrahedral coordination on melting. Although the five-coordinate MgCl 5 3– complex was not considered in the early literature, together with an increasing tendency to form a tetrahedrally coordinated complex with decreasing the MgCl 2 content in the mixture with alkali metal chloride systems, current work reconciles the results of most previous seemingly contradictory experimental studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗