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DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

Computational analysis of methods for reduction of induced drag

The purpose of this effort was to perform a computational flow analysis of a design concept centered around induced drag reduction and tip-vortex energy recovery. The flow model solves the unsteady three-dimensional Euler equations, discretized as a finite-volume method, utilizing a high-resolution approximate Riemann solver for cell interface flux definitions. The numerical scheme is an approximately-factored block LU implicit Newton iterative-refinement method. Multiblock domain decomposition is used to partition the field into an ordered arrangement of blocks. Three configurations are analyzed: a baseline fuselage-wing, a fuselage-wing-nacelle, and a fuselage-wing-nacelle-propfan. Aerodynamic force coefficients, propfan performance coefficients, and flowfield maps are used to qualitatively access design efficacy. Where appropriate, comparisons are made with available experimental data.

Janus, J. M.↗

NASA NTRS1998

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗

NASA NTRS1986

Implicit, vectorizable schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Two hybrid upwind models are defined for solving the Euler equations. The algorithms both employ approximate factorization (AF) in crossplane and symmetric block Gauss-Seidel relaxation in the third direction. One approach adds an additional factorization step to lower the number of required grid point operations for inversion of the block tridiagonal matrices; however, the move permits only one third of the operations to be vectorized. Finite difference solutions are calculated on a C-H-type grid, in this case enveloping a slender, sharp-edged delta wing. Sample data are provided for the calculated vortex flow for Re of 10,000, at a 20.5 deg angle of attack, represented in a crossflow velocity vector plot and in a spanwise pressure coefficient distribution. The AF scheme, without additional factorization, when used with a grid covering 51 x 51 x 72 points provides a convergent solution with no time step lasting longer than 0.00001 sec.

Liu, C. H.↗

NASA NTRS1992

Computation of unsteady flows over airfoils

Two methods are described for calculating unsteady flows over rapidly pitching airfoils. The first method is based on an interactive scheme in which the inviscid flow is obtained by a panel method. The boundary layer flow is computed by an interactive method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier-Stokes equations. The solution of these equations is obtained with an approximately factorized numerical algorithm, and with single block or multiple grids which enable grid embedding to enhance the resolution at isolated flow regions. In addition, the attached flow region can be computed by the numerical solution of compressible boundary layer equations. Unsteady pressure distributions obtained with both methods are compared with available experimental data.

Ekaterinaris, J. A.↗

NASA NTRS1989

A multigrid and upwind viscous flow solver on 3-D embedded and overlapped grids

A numerically efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flow about complex configurations with topologically different components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually with no significant restrictions. The Navier-Stokes equations are solved by an implicit, approximately factored, upwind, finite-volume scheme. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the holes created in the computational domain by the embedded and overlapped grids. The convergence is accelerated by a multigrid algorithm despite the existence of such holes. The solution for s supersonic flow past a blunt-nose-cylinder at high angle-of-attack is obtained using a C-O grid embedded in a global Cartesian grid.

Baysal, Oktay↗

NASA NTRS1991

Hydrotropism and its interaction with gravitropism in maize roots

We have partially characterized root hydrotropism and its interaction with gravitropism in maize (Zea mays L.). Roots of Golden Cross Bantam 70, which require light for orthogravitropism, showed positive hydrotropism; bending upward when placed horizontally below a hydrostimulant (moist cheesecloth) in 85% relative humidity (RH) and in total darkness. However, the light-exposed roots of Golden Cross Bantam 70 or roots of a normal maize cultivar, Burpee Snow Cross, showed positive gravitropism under the same conditions; bending downward when placed horizontally below the hydrostimulant in 85% RH. Light-exposed roots of Golden Cross Bantam 70 placed at 70 degrees below the horizontal plane responded positively hydrotropically, but gravitropism overcame the hydrotropism when the roots were placed at 45 degrees below the horizontal. Roots placed vertically with the tip down in 85% RH bent to the side toward the hydrostimulant in both cultivars, and light conditions did not affect the response. Such vertical roots did not respond when the humidity was maintained near saturation. These results suggest that hydrotropic and gravitropic responses interact with one another depending on the intensity of one or both factors. Removal of the approximately 1.5 millimeter root tip blocked both hydrotropic and gravitropic responses in the two cultivars. However, removal of visible root tip mucilage did not affect hydrotropism or gravitropism in either cultivar.

NASA Program Space Biology↗

NASA NTRS1993

Navier-Stokes simulation of external/internal transonic flow on the forebody/inlet of the AV-8B Harrier II

In this work, the computation of combined external/internal transonic flow on the complex forebody/inlet configuration of the AV-8B Harrier II is performed. The actual aircraft has been measured and its surface and surrounding domain, in which the fuselage and inlet have a common wall, have been described using structured grids. The 'thin-layer' Navier-Stokes equations were used to model the flow along with the Chimera embedded multi-block technique. A fully conservative, alternating direction implicit (ADI), approximately factored, partially fluxsplit algorithm was employed to perform the computation. Comparisons to some experimental wind tunnel data yielded good agreement for flow at zero incidence and angle of attack. The aim of this paper is to provide a methodology or computational tool for the numerical solution of complex external/internal flows.

Mysko, Stephen J.↗

NASA NTRS1981

BGRID: A block-structured grid generation code for wing sections

The operation of the BGRID computer program is described for generating block-structured grids. Examples are provided to illustrate the code input and output. The application of a fully implicit AF (approximation factorization)-based computer code, called TWINGB (Transonic WING), for solving the 3D transonic full potential equation in conservation form on block-structured grids is also discussed.

Chen, H. C.↗

NASA NTRS1990

Three-dimensional Euler time accurate simulations of fan rotor-stator interactions

A numerical method useful to describe unsteady 3-D flow fields within turbomachinery stages is presented. The method solves the compressible, time dependent, Euler conservation equations with a finite volume, flux splitting, total variation diminishing, approximately factored, implicit scheme. Multiblock composite gridding is used to partition the flow field into a specified arrangement of blocks with static and dynamic interfaces. The code is optimized to take full advantage of the processing power and speed of the Cray Y/MP supercomputer. The method is applied to the computation of the flow field within a single stage, axial flow fan, thus reproducing the unsteady 3-D rotor-stator interaction.

Boretti, A. A.↗

NASA NTRS1994

Theoretical investigation of variable periodicity (graded) multilayers for hard x ray applications

The objective of this research was to investigate the possibility of increasing the useful bandwidth of multilayer mirrors. Mirrors 'constructed' with non-periodically spaced reflecting surfaces were considered. These structures included depth-graded and laterally-graded mirrors as well as those with reflectors located via a log-periodic spacing rule. No enhancement of bandwidth resulted from simulations of simple versions of any of the three non-periodic mirrors. However, certain depth-graded structures did exhibit reflectances essentially the same as from uniform mirrors. Moreover, it was found that some control was possible regarding the location (with respect to energy) of the maximum reflectance peak. Effective bandwidth was increased when composite models were simulated. In two of the cases studied, bandwidth was enhanced by a factor of approximately 3. One model consisted of a depth-graded mirror constructed with three separately defined structures, or blocks. Each block consisted of two layer-pairs repeated three times. Then, the entire 18 layer-pair group was repeated several times. Simulation of this 3 block depth-graded configuration yielded three reflectance peaks, one representative of each depth-graded block. The other configurations resulting in enhanced bandwidth assumed independently constructed mirrors immediately adjacent to each other and sharing the same substrate. Reflectance peaks from each mirror appeared in the response. Both basic models show greatly enhanced effective bandwidths even though the reflectance curves appear as non-overlapping for these specific models. Additionally, these configurations are realizable. Details are contained in the section, DESIGN SIMULATIONS.

Kinney, Ralph A.↗

NASA NTRS2001

Transmission Properties of Zitex in the Infrared to Submillimeter

The results of measurements of the refractive index and power absorption coefficient of Zitex at 290 K, 77 K, and 4 K in the spectral region from 1 to 1000 microns are presented. Zitex is a porous Teflon sheet with a filling factor of approximately 50%, and is manufactured in several varieties as a filter paper. Zitex is found to be an effective infrared radiation block, with thin (200 micrometer) sheets transmitting less than 1% in the 1-50 micrometer range while absorbing <10% at wavelengths longer than 200 micrometers. Some variation in the cutoff wavelength is seen, tending to be a shorter wavelength cutoff for a smaller pore size. Additionally, the thermal conductivity of Zitex at cryogenic temperatures has been measured, and is found to be roughly one-half that of bulk Teflon.

Benford, D. J.↗

NASA NTRS1998

Venous levels of shear support neutrophil-platelet adhesion and neutrophil aggregation in blood via P-selectin and beta2-integrin

BACKGROUND: After activation, platelets adhere to neutrophils via P-selectin and beta2-integrin. The molecular mechanisms and adhesion events in whole blood exposed to venous levels of hydrodynamic shear in the absence of exogenous activation remain unknown. METHODS AND RESULTS: Whole blood was sheared at approximately 100 s(-1). The kinetics of neutrophil-platelet adhesion and neutrophil aggregation were measured in real time by flow cytometry. P-selectin was upregulated to the platelet surface in response to shear and was the primary factor mediating neutrophil-platelet adhesion. The extent of neutrophil aggregation increased linearly with platelet adhesion to neutrophils. Blocking either P-selectin, its glycoprotein ligand PSGL-1, or both simultaneously by preincubation with a monoclonal antibody resulted in equivalent inhibition of neutrophil-platelet adhesion (approximately 30%) and neutrophil aggregation (approximately 70%). The residual amount of neutrophil adhesion was blocked with anti-CD11b/CD18. Treatment of blood with prostacyclin analogue ZK36374, which raises cAMP levels in platelets, blocked P-selectin upregulation and neutrophil aggregation to baseline. Complete abrogation of platelet-neutrophil adhesion required both ZK36374 and anti-CD18. Electron microscopic observations of fixed blood specimens revealed that platelets augmented neutrophil aggregation both by forming bridges between neutrophils and through contact-mediated activation. CONCLUSIONS: The results are consistent with a model in which venous levels of shear support platelet adherence to neutrophils via P-selectin binding PSGL-1. This interaction alone is sufficient to mediate neutrophil aggregation. Abrogation of platelet adhesion and aggregation requires blocking Mac-1 in addition to PSGL-1 or P-selectin. The described mechanisms are likely of key importance in the pathogenesis and progression of thrombotic disorders that are exacerbated by leukocyte-platelet aggregation.

NASA Discipline Cell Biology↗

NASA NTRS1998

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗

NASA NTRS1983

Improved relaxation schemes for transonic potential calculations

A block relaxation scheme, grouped in a red-black ordering, is applied to transonic airfoil calculations using body fitted coordinates. The scheme is simple and is easily vectorizable. Detailed comparisons with Approximate Factorization Method (AF2) are presented and it is shown that the improved relaxation scheme is competitive in all cases considered. Transonic results, of engineering accuracy, on an 0-type grid of 149 x 30 points, are ususally obtained within two hundred iterations (approximately 40 seconds on Cyber 175).

Hafez, M.↗

NASA NTRS2001

Performance Testing of a Lightweight, High Efficiency 95 K Cryocooler

Performance data are presented for a flight-like, lightweight, high efficiency pulse tube cryogenic cooler. The cooler has a mass of less than 4.0 kg, and an efficiency of 12 W/W, which is 18% of Carnot at 95 K, nearly double the efficiency of previous cooler designs, The mass of the cooler has been reduced by approximately a factor of three. The design point cooling power is 10 watts at 95 K at a heat rejection temperature of 300 K. The no-load temperature is 45 K. The compressor is built by Hymatic Engineering, UK, and is of a horizontally opposed piston design using flexure bearings. The vertical pulse tube is built by TRW with the heat exchanger or cold block located approximately mid-way along the tube. The final assembly and integration is also performed by TRW. The inertance tube and dead volume are contained within one of the compressor end caps. The cooler was developed by TRW under a joint NASA-DOD program, and has a goal of 10 yr operating lifetime. Potential NASA applications will focus on using coolers of this type in Zero boil off (ZBO) cryogen storage topologies for next generation launch vehicles. Zero boil off systems will feature significant reductions in tank size and Initial Mass to Low Earth Orbit (IMLEO), thereby significantly reducing the cost of access to space, and enabling future missions. The coolers can be used directly in liquid oxygen (LOx) or liquid methane ZBO systems, as shield coolers in liquid hydrogen tanks, or as first stage coolers in two-stage liquid hydrogen (LH2) ZBO cooler systems. Finally, the coolers could find applications in exploration missions where either propellants or breathable oxygen are extracted from the planetary atmosphere using a Sabatier or similar process. The gases could then be liquefied for storage either directly in return vehicle propellant tanks or on the planetary surface. Data presented were taken with the cooler operating in a vacuum of 10 (exp -5) torr, at controlled rejection temperatures from 300 K down to 275 K using a cold water heat exchanger bolted to the cooler. Heat loads were varied between 0.5 W and 15 W by supplying current to a 50 omega resistor mounted on a copper cold plate which was bolted to the cooler cold block. Silicon diodes mounted on both the cold plate and the heat exchanger provided accurate temperature measurement to within plus or minus 0.25 K and plus or minus 0.5 K respectively, up to 100 K with plus or minus 1% accuracy above 100 K. Input power to the compressor was limited to 180 W, corresponding to a maximum stroke of 80%.

Salerno, Lou↗

NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗

NASA NTRS1996

A 850 GHz SIS receiver employing silicon micro-machining technology

A 850 GHz superconductor-insulator-superconductor (SIS) heterodyne receiver which uses a radiofrequency tuned niobium tunnel junction fabricated on a 1 micron thick silicon nitrate membrane, is reported. From video and heterodyne measurements, it was calculated that the niobium film loss in the radiofrequency matching network is about 6.8 dB at 822 GHz. These results are approximately a factor of two higher than the theoretical loss predicted by the Mattis-Bardeen theory in the extreme anomalous limit. The junction design and the receiver configuration are described, including the mixer block, the membrane construction and the cooled optics. The performance tests using a Fourier transform spectrometer to measure the response of the radiofrequency matching network, and the SIS simulations of the receiver response to cold and hot loads, the infrared noise contribution and the overall mixer conversion efficiency, are reported. It is concluded that the receiver response is limited by the absorption loss in the radiofrequency matching network.

Kooi, J. W.↗