Search NASA⌕ Search

SEARCH · Search NASA

Results for “mixed 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

An improved method for predicting the effects of flight on jet mixing noise

A method for predicting the effects of flight on jet mixing noise has been developed on the basis of the jet noise theory of Ffowcs-Williams (1963) and data derived from model-jet/free-jet simulated flight tests. Predicted and experimental values are compared for the J85 turbojet engine on the Bertin Aerotrain, the low-bypass refanned JT8D engine on a DC-9, and the high-bypass JT9D engine on a DC-10. Over the jet velocity range from 280 to 680 m/sec, the predictions show a standard deviation of 1.5 dB.

Stone, J. R.↗

A O(1/k{sup 3/2}) hybrid proximal extragradient primal–dual interior point method for nonlinear monotone mixed complementarity problems

We present a Newton-type hybrid proximal extragradient primal–dual interior point method for solving smooth monotone mixed complementarity problems. Dual variables for the nonnegativity constraints are introduced. The ergodic complexity of the method is O(1/k{sup 3/2}). The method performs two types of iterations: underelaxed hybrid proximal extragradient iterations and short-steps primal–dual interior point iterations.

97 MATHEMATICS AND COMPUTING↗

Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics

Here, the exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron–ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron–nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The arbitrary order mixed mimetic finite difference method for the diffusion equation

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux and scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.

97 MATHEMATICS AND COMPUTING↗

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

97 MATHEMATICS AND COMPUTING↗

Generalization of mixed multiscale finite element methods with applications

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii

97 MATHEMATICS AND COMPUTING↗

An empirical method for predicting the mixing noise levels of subsonic circular and coaxial jets

An empirical method for predicting the static free field source noise levels of subsonic circular and coaxial jet flow streams is presented. The method was developed from an extensive data base of 817 jet tests obtained from five different government and industry sources in three nations. The prediction method defines the jet noise in terms of four components which are overall power level, power spectrum level, directivity index, and relative spectrum level. The values of these noise level components are defined on a grid consisting of seven frequency parameter values (Strouhal numbers) and seven directivity angles. The value of the noise level at each of these grid points is called a noise level coordinate and was defined as a function of five jet exhaust flow state parameters which are equivalent jet velocity, equivalent jet total temperature, the velocity ratio (outer stream to inner stream), temperature ratio, and area ratio. The functions were obtained by curve fitting in a least squares sense the noise level coordinates from the data base in a five dimensional flow state space using a third order Taylor series. The noise level coordinates define the component noise levels for all frequencies and directivities through a bicubic spline function.

Russell, J. W.↗

Mixed finite-element method for multi-term time-fractional diffusion and diffusion-wave equations

In this paper, numerical theory based on the mixed finite-element method and finite difference analog of the Caputo fractional derivative for multi-term time-fractional diffusion equations and diffusion-wave equations is analyzed. The unconditional stability and convergence results are proved for the two resulting fully discrete schemes. Finally, the obtained results are supported by numerical experiments carried out for some test problems.

97 MATHEMATICS AND COMPUTING↗

Scalable algorithms for three-field mixed finite element coupled poromechanics

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 x 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. In conclusion, the performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

42 ENGINEERING↗

Testing of the Defense Waste Processing Facility Cold Chemical Dissolution Method in Sludge Batch 9 Qualification

For each sludge batch that is processed in the Defense Waste Processing Facility (DWPF), the Savannah River National Laboratory (SRNL) tests the applicability of the digestion methods used by the DWPF Laboratory for elemental analysis of Sludge Receipt and Adjustment Tank (SRAT) Receipt samples and SRAT Product process control samples. DWPF SRAT samples are typically dissolved using a method referred to as the DWPF Cold Chemical or Cold Chem Method (CC), (see DWPF Procedure SW4- 15.201). Testing indicates that the CC method produced mixed results. The CC method did not result in complete dissolution of either the SRAT Receipt or SRAT Product with some fine, dark solids remaining. However, elemental analyses did not reveal extreme biases for the major elements in the sludge when compared with analyses obtained following dissolution by hot aqua regia (AR) or sodium peroxide fusion (PF) methods. The CC elemental analyses agreed with the AR and PF methods well enough that it should be adequate for routine process control analyses in the DWPF after much more extensive side-by-side tests of the CC method and the PF method are performed on the first 10 SRAT cycles of the Sludge Batch 9 (SB9) campaign. The DWPF Laboratory should continue with their plans for further tests of the CC method during these 10 SRAT cycles.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Systems and methods for thermal imaging technique for measuring mixing of fluids

Systems and methods for thermal imaging for measuring mixing of fluids are provided. In one embodiment, a method for measuring mixing of gaseous fluids using thermal imaging comprises: positioning a thermal test medium parallel to a direction gaseous fluid flow from an outlet vent of a momentum source, wherein when the source is operating, the fluid flows across a surface of the medium; obtaining an ambient temperature value from a baseline thermal image of the surface; obtaining at least one operational thermal image of the surface when the fluid is flowing from the outlet vent across the surface, wherein the fluid has a temperature different than the ambient temperature; and calculating at least one temperature-difference fraction associated with at least a first position on the surface based on a difference between temperature measurements obtained from the at least one operational thermal image and the ambient temperature value.

42 ENGINEERING↗

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Tamma, Kumar K.↗

Comparative Performance of Engines Using a Carburetor, Manifold Injection, and Cylinder Injection

The comparative performance was determined of engines using three methods of mixing the fuel and the air: the use of a carburetor, manifold injection, and cylinder injection. The tests were made of a single-cylinder engine with a Wright 1820-G air-cooled cylinder. Each method of mixing the fuel and the air was investigated over a range of fuel-air ratios from 0.10 to the limit of stable operation and at engine speeds of 1,500 and 1,900 r.p.m. The comparative performance with a fuel-air ratio of 0.08 was investigated for speeds from 1,300 to 1,900 r.p.m. The results show that the power obtained with each method closely followed the volumetric efficiency; the power was therefore the highest with cylinder injection because this method had less manifold restriction. The values of minimum specific fuel consumption obtained with each method of mixing of fuel and air were the same. For the same engine and cooling conditions, the cylinder temperatures are the same regardless of the method used for mixing the fuel and the air.

Schey, Oscar W↗

Methods of testing parameterizations: Vertical ocean mixing

The ocean's velocity field is characterized by an exceptional variety of scales. While the small-scale oceanic turbulence responsible for the vertical mixing in the ocean is of scales a few centimeters and smaller, the oceanic general circulation is characterized by horizontal scales of thousands of kilometers. In oceanic general circulation models that are typically run today, the vertical structure of the ocean is represented by a few tens of discrete grid points. Such models cannot explicitly model the small-scale mixing processes, and must, therefore, find ways to parameterize them in terms of the larger-scale fields. Finding a parameterization that is both reliable and plausible to use in ocean models is not a simple task. Vertical mixing in the ocean is the combined result of many complex processes, and, in fact, mixing is one of the less known and less understood aspects of the oceanic circulation. In present models of the oceanic circulation, the many complex processes responsible for vertical mixing are often parameterized in an oversimplified manner. Yet, finding an adequate parameterization of vertical ocean mixing is crucial to the successful application of ocean models to climate studies. The results of general circulation models for quantities that are of particular interest to climate studies, such as the meridional heat flux carried by the ocean, are quite sensitive to the strength of the vertical mixing. We try to examine the difficulties in choosing an appropriate vertical mixing parameterization, and the methods that are available for validating different parameterizations by comparing model results to oceanographic data. First, some of the physical processes responsible for vertically mixing the ocean are briefly mentioned, and some possible approaches to the parameterization of these processes in oceanographic general circulation models are described in the following section. We then discuss the role of the vertical mixing in the physics of the large-scale ocean circulation, and examine methods of validating mixing parameterizations using large-scale ocean models.

Tziperman, Eli↗

Machine learning aided line intensity ratio method for helium–hydrogen mixed recombining plasmas

The helium line intensity ratio (LIR) with the help of a collisional radiative (CR) model has long been used to measure the electron density, n e , and temperature, T e , and its potential and limitations for fusion applications have been discussed. However, it has been reported that the CR model approach leads to deviations in helium–hydrogen mixed plasmas and/or recombining plasmas. In this study, a machine learning (ML) aided LIR method is used to measure n e and T e from spectroscopic data of helium–hydrogen mixed recombining plasmas in the divertor simulator Magnum-PSI. To analyze mixed plasmas, which have more complex spectral shapes, the spectroscopy data were used directly for training instead of separating the intensities of each line. Finally, it is shown that the ML approach can provide a robust and simpler analysis method to deduce n e and T e from the visible emissions in helium–hydrogen mixed plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlocal and Mixed-Locality Multiscale Finite Element Methods

In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, in this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.

97 MATHEMATICS AND COMPUTING↗

An improved method for predicting the effects of flight on jet mixing noise

The NASA method (1976) for predicting the effects of flight on jet mixing noise was improved. The earlier method agreed reasonably well with experimental flight data for jet velocities up to about 520 m/sec (approximately 1700 ft/sec). The poorer agreement at high jet velocities appeared to be due primarily to the manner in which supersonic convection effects were formulated. The purely empirical supersonic convection formulation of the earlier method was replaced by one based on theoretical considerations. Other improvements of an empirical nature included were based on model-jet/free-jet simulated flight tests. The revised prediction method is presented and compared with experimental data obtained from the Bertin Aerotrain with a J85 engine, the DC-10 airplane with JT9D engines, and the DC-9 airplane with refanned JT8D engines. It is shown that the new method agrees better with the data base than a recently proposed SAE method.

Stone, J. R.↗

The design and development of transonic multistage compressors

The development of the transonic multistage compressor is reviewed. Changing trends in design and performance parameters are noted. These changes are related to advances in compressor aerodynamics, computational fluid mechanics and other enabling technologies. The parameters normally given to the designer and those that need to be established during the design process are identified. Criteria and procedures used in the selection of these parameters are presented. The selection of tip speed, aerodynamic loading, flowpath geometry, incidence and deviation angles, blade/vane geometry, blade/vane solidity, stage reaction, aerodynamic blockage, inlet flow per unit annulus area, stage/overall velocity ratio, and aerodynamic losses are considered. Trends in these parameters both spanwise and axially through the machine are highlighted. The effects of flow mixing and methods for accounting for the mixing in the design process are discussed.

Ball, C. L.↗