A GPU-Enabled Higher Order Mixed Finite Element Method for Pulsed Power ICF Target Design
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Physics - Plasma physics↗
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On Hybrid and mixed finite element methods
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Pian, T. H. H.↗
A mixed pseudospectral/finite difference method for a thermally driven fluid in a nonuniform gravitational field
A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modelled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.
Macaraeg, M. G.↗
A mixed pseudospectral/finite difference method for a thermally driven fluid in a nonuniform gravitational field
A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later Shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modeled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.
Macaraeg, M. G.↗
A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell
For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.
Macaraeg, M. G.↗
A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection
A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.
Buell, Jeffrey C.↗
Numerical Analysis Of Flows With FIDAP
Report presents an evaluation of accuracy of Fluid Dynamics Package (FIDAP) computer program. Finite-element code for analysis of flows of incompressible fluids and transfers of heat in multidimensional domains. Includes both available methods for treatment of spurious numerical coupling between simulated velocity and simulated pressure; namely, penalty method and mixed-interpolation method with variable choices of interpolation polynomials for velocity and pressure. Streamwise upwind (STU) method included as option for flows dominated by convection.
Sohn, Jeong L.↗
Mixed-mode bending method for delamination testing
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Reeder, James R.↗
In Situ Testing Methods for Mixed-Mode Harsh Environments
A review of the radiation effects investigation capabilities of the JPL Dynamitron Accelerator Facility are discussed. A process for its use in performing total ionizing dose (TID) studies are outlined. The results of radiation effects in complicated test systems where device effects may occur due to local system irradiation are also presented.
Wong, A. T.↗
Comparison of Two Approaches to Constructing Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Methods for Mixed-Element Grids
In this paper, we introduce a third-order nodal-gradient cell-centered finite volume scheme applicable to mixed-element grids based on a single numerical flux per face. Previously, we considered a split-quadrilateral-face approach, where we split each quadrilateral face of a non-tetrahedral cell into two triangles and then apply second- and third-order schemes designed for tetrahedral grids. This approach is relatively simple to implement but expensive because it requires two numerical flux evaluations per quadrilateral face. In this study, we consider another approach, where the surface flux quadrature is performed with a single numerical flux per face with flux corrections. It requires a 3×3 correction matrix to be stored at each face but is more economical than the split-quadrilateral-face approach. The two approaches are compared for three-dimensional flows on irregular hexahedral grids, and their relative merits are discussed.
Third-order scheme↗
Development of an Empirical Methods for Predicting Jet Mixing Noise of Cold Flow Rectangular Jets
This report presents an empirical method for predicting the jet mixing noise levels of cold flow rectangular jets. The report presents a detailed analysis of the methodology used in development of the prediction method. The empirical correlations used are based on narrow band acoustic data for cold flow rectangular model nozzle tests conducted in the NASA Langley Jet Noise Laboratory. There were 20 separate nozzle test operating conditions. For each operating condition 60 Hz bandwidth microphone measurements were made over a frequency range from 0 to 60,000 Hz. Measurements were performed at 16 polar directivity angles ranging from 45 degrees to 157.5 degrees. At each polar directivity angle, measurements were made at 9 azimuth directivity angles. The report shows the methods employed to remove screech tones and shock noise from the data in order to obtain the jet mixing noise component. The jet mixing noise was defined in terms of one third octave band spectral content, polar and azimuth directivity, and overall power level. Empirical correlations were performed over the range of test conditions to define each of these jet mixing noise parameters as a function of aspect ratio, jet velocity, and polar and azimuth directivity angles. The report presents the method for predicting the overall power level, the average polar directivity, the azimuth directivity and the location and shape of the spectra for jet mixing noise of cold flow rectangular jets.
Russell, James W.↗
Material nonlinear analysis via mixed-iterative finite element method
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Sutjahjo, Edhi↗
Synthesis of soluble conducting polymers by acoustic mixing
A method including combining an aniline monomer, an oxidant, water and an organic solvent; subjecting the combination to acoustic mixing to form an emulsion; and recovering a polyaniliine from the combination. A method including combining a aniline monomer, an oxidant, water and an organic solvent; forming a polyaniline by acoustic mixing the combination; and recovering the polyaniliine from the combination. A method including forming a combination of an aniline monomer, an oxidant, water and an organic solvent in the absence of an emulsifier; acoustic mixing the combination for a time period to form a polyaniline; and recovering a polyaniliine from the combination.
36 MATERIALS SCIENCE↗
Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method
Optimal planning and design of microgrids are priorities in the electrification of off-grid areas. Indeed, in one of the Sustainable Development Goals (SDG 7), the UN recommends universal access to electricity for all at the lowest cost. Several optimization methods with different strategies have been proposed in the literature as ways to achieve this goal. This paper proposes a microgrid installation and planning model based on a combination of several techniques. The programming language Python 3.10 was used in conjunction with machine learning techniques such as unsupervised learning based on K-means clustering and deterministic optimization methods based on mixed linear programming. These methods were complemented by the open-source spatial method for optimal electrification planning: onsset. Four levels of study were carried out. The first level consisted of simulating the model obtained with a cluster, which is considered based on the elbow and k-means clustering method as a case study. The second level involved sizing the microgrid with a capacity of 40 kW and optimizing all the resources available on site. The example of the different resources in the Togo case was considered. At the third level, the work consisted of proposing an optimal connection model for the microgrid based on voltage stability constraints and considering, above all, the capacity limit of the source substation. Finally, the fourth level involved a planning study of electrification strategies based mainly on microgrids according to the study scenario. The results of the first level of study enabled us to obtain an optimal location for the centroid of the cluster under consideration, according to the different load positions of this cluster. Then, the results of the second level of study were used to highlight the optimal resources obtained and proposed by the optimization model formulated based on the various technology costs, such as investment, maintenance, and operating costs, which were based on the technical limits of the various technologies. In these results, solar systems account for 80% of the maximum load considered, compared to 7.5% for wind systems and 12.5% for battery systems. Next, an optimal microgrid connection model was proposed based on the constraints of a voltage stability limit estimated to be 10% of the maximum voltage drop. The results obtained for the third level of study enabled us to present selective results for load nodes in relation to the source station node. Finally, the last results made it possible to plan electrification using different network technologies and systems in the short and long term. The case study of Togo was taken into account. The various results obtained from the different techniques provide the necessary leads for a feasibility study for optimal electrification of off-grid areas using microgrid systems.
24 POWER TRANSMISSION AND DISTRIBUTION↗
High-order gradients with the shifted boundary method: An embedded enriched mixed formulation for elliptic PDEs
Here, we propose an extension of the embedded boundary method known as “shifted boundary method” to elliptic diffusion equations in mixed form (e.g., Darcy flow, heat diffusion problems with rough coefficients, etc.). Our aim is to obtain an improved formulation that, for linear finite elements, is at least second-order accurate for both flux and primary variable, when either Dirichlet or Neumann boundary conditions are applied. Following previous work of Nishikawa and Mazaheri in the context of residual distribution methods, we consider the mixed form of the diffusion equation (i.e., with Darcy-type operators), and introduce an enrichment of the primary variable. This enrichment is obtained exploiting the relation between the primary variable and the flux variable, which is explicitly available at nodes in the mixed formulation. The proposed enrichment mimics a formally quadratic pressure approximation, although only nodal unknowns are stored, similar to a linear finite element approximation. We consider both continuous and discontinuous finite element approximations and present two approaches: a non-symmetric enrichment, which, as in the original references, only improves the consistency of the overall method; and a symmetric enrichment, which enables a full error analysis in the classical finite element context. Combined with the shifted boundary method, these two approaches are extended to high-order embedded computations, and enable the approximation of both primary and flux (gradient) variables with second-order accuracy, independently on the type of boundary conditions applied. We also show that the primary variable is third-order accurate, when pure Dirichlet boundary conditions are embedded.
97 MATHEMATICS AND COMPUTING↗
A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry
We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The evaluation of a metered mixer for RTV silicone for RSRM nozzle backfill operations
Metered mixing specifically for the RSRM backfill operation was investigated. Projected advantages were the elimination of waste RTV silicone produced in the operation and the elimination of entrapped air during the mix. Although metered mixing proved to be a viable method for mixing the Dow Corning DC 90-0006 rubber with its catalyst, applying the technology to the RSRM backfill operation has several disadvantages that are decisive. Use of a metered mixer would increase the amount of material that was being scraped for each backfill and increase the amount of time required to clean up the equipment after each operation. Therefore, use of metered static mixers is not recommended for use in the RSRM nozzle backfill operations. Because metered mixers proved to have significant disadvantages other methods of mixing and dispensing the RTV during the backfill operation are being investigated, and will be reported in a separate document.
Wardell, T. C.↗
Scanning angle Raman spectroscopy: A nondestructive method for simultaneously determining mixed polymer fractional composition and film thickness
A scanning angle (SA) Raman spectroscopy method was developed to simultaneously measure the chemical composition and thickness of waveguide mixed polymer films with varying fractional compositions. In order to test the method, six films of polystyrene-block-poly(methyl methacrylate), some mixed with poly(methyl methacrylate) homopolymer (PS-b-PMMA:PMMA), and two films of poly(2-vinylnapthalene)-block-poly(methyl methacrylate) (P2VN-b-PMMA) were prepared. The film thickness ranged from 495 to 971 nm. The chemical composition and thickness of PS-b-PMMA:PMMA films was varied by the addition of the PMMA homopolymer and annealing the films in toluene. SA Raman peak amplitude ratios (1001 cm -1 for PS, 812 cm -1 for PMMA, and 1388 cm -1 for P2VN) were used to calculate the refractive index of the polymer film, an input parameter in calculations of the sum square electric field (SSEF). The film thickness was determined by SSEF models of the experimental Raman amplitudes versus the incident angle of light. The average film thickness determined by the developed SA Raman spectroscopy method was within 5% of the value determined by optical profilometry. In conclusion, SA Raman spectroscopy will be useful for in situ label-free analyses of mixed polymer waveguide films.
36 MATERIALS SCIENCE↗