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At least 811 records · Page 45

An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. In particular, we consider stochastic elliptic PDEs with an affine dependence on the random variable. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗

Validation of general purpose mathematical efficiency modeling with ISOCS - 15579

Gamma spectroscopy is a commonly used method for radioactive waste characterization and activity determination in in-situ objects. The gamma rays emitted by radionuclides in the waste container matrix are highly penetrating and can be measured using one or more gamma ray detectors, thus allowing for a passive nondestructive assay. One problem is that a source based calibration of full energy peak efficiency can be difficult or impractical because of the large size and/or an unusual shape of the sample geometry. One attractive solution is to use mathematical efficiency modeling to calculate the full energy peak efficiency. The In-Situ Object Calibration Software (ISOCS) has successfully been used for more than a decade for mathematical efficiency modeling of template based geometries. Templates include the most common objects in waste characterization and D and D, including but not limited to: boxes, drums, and pipes with hotspots, beams, tanks and walls. Scenarios exist where these templates cannot model the desired measurement geometry. Canberra has developed a general purpose version of ISOCS where primitive objects can be combined into practically any geometry. The primitive objects are right circular cylinder, right elliptical cylinder, right circular cone, right elliptical cone, sphere, spheroid, ellipsoid, box (rectangular parallelepiped), torus, and beaker (any cylindrical symmetric object). Multiple primitive objects can be combined using the priority scheme and cut by planes into almost any desired shape. In addition, multiple objects can be defined in the same scene, for example cylinders next to each other or a pipe and a box. Collimators can be constructed as easily as in template based ISOCS. The ray tracing algorithm in ISOCS has been extended to support the new primitive objects for attenuation calculation between the radioactive source and the detector end cap. The new version uses the same vacuum efficiency response, or characterization, in the energy range 10 - 7000 keV of individual detectors to be able to calculate the efficiency as accurately as possible. MCNP has been shown to be able to calculate detection efficiencies for any geometry and the new version of ISOCS have been validated to MCNP. The vacuum efficiency is based on an MCNP model and this model was the base for constructing an identical model in MCNP as in ISOCS. The calculated efficiencies from the two codes have been compared and the agreement is within 3% except for the lowest energies for one geometry. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation

A C++ library (called Eshelby ) was implemented in fiscal year 2015 based upon the formulas documented in this report. The library implements a generalized version of Eshelby's inclusion problem. The library was written as a set of functions which can be called from another program; the principle intended use cases are kinetic models of precipitate formation in zirconium claddings where use of the Eshelby library provides needed elastic energy density calculations, as well as calculations of stress and strain in and around precipitates; it is intended that the library will be made open source. For isotropic inclusions in the form of oblate and prolate ellipsoids, the Eshelby library can be used for nearly any relevant/appropriate shape parameters to calculate strains, stresses and energy density at interior and exterior points. The Eshelby library uses a combination of analytical formulas and numerical routines making it very extensible. For example, the library can can easily be extended to include inclusions such as spheres since analytical expressions exist for the required elliptic integrals; similarly, general ellipsoids do not have analytical results for the required elliptic integrals but those integrals can be numerically evaluated and thus fit naturally into the Eshelby library. This report documents all formulas implemented in the Eshelby library and presents some demonstration calculations relevant to the intended application.

97 MATHEMATICS AND COMPUTING↗

Large-scale assembly bias of dark matter halos

We present precise measurements of the assembly bias of dark matter halos, i.e. the dependence of halo bias on other properties than the mass, using curved 'separate universe' N-body simulations which effectively incorporate an infinite-wavelength matter overdensity into the background density. This method measures the LIMD (local-in-matter-density) bias parameters b {sub n} in the large-scale limit. We focus on the dependence of the first two Eulerian biases b {sup E} {sup {sub 1}} and b {sup E} {sup {sub 2}} on four halo properties: the concentration, spin, mass accretion rate, and ellipticity. We quantitatively compare our results with previous works in which assembly bias was measured on fairly small scales. Despite this difference, our findings are in good agreement with previous results. We also look at the joint dependence of bias on two halo properties in addition to the mass. Finally, using the excursion set peaks model, we attempt to shed new insights on how assembly bias arises in this analytical model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Wake Structure Induced by Seal Whisker: Effects of Angle of Incidence

Seal whiskers have been found to produce unique wake flow structures that minimize self-induced vibration and reduce drag. The cause of these wake features are due to the peculiar three-dimensional morphology of the whisker surface. The whisker can be defined as an elliptical cross section with variation in the major and minor axis of the ellipse along the length of the whisker as well as rotation of the elliptical plane with respect to the whisker axis, angle of incidence. While the effects of several dominant parameters of the whisker morphology have been studied, the effect of the rotation of the elliptical plane has not been well understood. This paper will examine the influence of the angle of incidence on the wake flow structure through series of water channel studies. Several models of whisker-like geometries will be tested which isolate the rotation angle as the only variation between models. The wake structure behind each seal whisker model will be measured through particle image velocimetry (PIV). The different models’ wake structures will be compared identifying the effect of angle of incidence on the wake structure. Angle of incidence was found to influence the wake structure through reorganization of velocity patterns, reduction of recovery length and modification of magnitude of Tu. These results help provide a more complete understanding of the seal whisker geometry relationship to wake structure and can provide insight into design practices for application of whisker geometery to various engineering problems.

vortex induced vibration↗

Numerical modeling of laser thermal propulsion flows

An review of the problems associated with modeling laser thermal propulsion flows, a synopsis of the status of such models, and the attributes of a successful model are presented. The continuous gaseous hydrogen laser-supported combustion wave (LSCW) thruster, for which a high-energy laser system (preferably space-based) should exist by the time the propulsion technology is developed, is considered in particular. The model proposed by Raizer (1970) is based on the assumptions of one-dimensional flow at constant pressure with heat conduction as the principal heat transfer mechanism. Consideration is given to subsequent models which account for radiative transfer into the ambient gas; provide a two-dimensional generalization of Raizer's analysis for the subsonic propagation of laser sparks in air; include the effect of forward plasma radiation in a one-dimensional model; and attempt a time-dependent (elliptic) solution of the full Navier-Stokes equations for the flow in a simple axisymmetric thruster. Attention is also given to thruster and nozzle flow models and thermodynamic and transport properties.

Mccay, T. D.↗

Comparison of multigrid algorithms for high‐order continuous finite element discretizations

Summary We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: (1) high‐order h ‐multigrid, which uses high‐order interpolation and restriction between geometrically coarsened meshes; (2) p ‐multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different‐order basis functions; and (3) a first‐order approximation multigrid preconditioner constructed using the nodes of the high‐order discretization. This latter approach is often combined with algebraic multigrid for the low‐order operator and is attractive for high‐order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both h ‐multigrid and p ‐multigrid work well; the first‐order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and symmetric successive over‐relaxation smoothing outperform Jacobi smoothing. While all of the tested methods converge in a mesh‐independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared with using multigrid as a solver. Copyright © 2015 John Wiley & Sons, Ltd.

Sundar, Hari↗

Optical properties of magnetic photonic crystals with an arbitrary magnetization orientation

We have studied the peculiarities of diffraction of light in magnetic photonic crystals at large values of magnetooptical activity parameter and modulation depth. We have considered the case of an arbitrary angle between the directions of the external static magnetic field and the normal to the layer. The problem has been solved by the modified Ambartsumyan layer summation method. It has been shown that the given system is nonreciprocal with respect to not only circular, but linear polarizations also. In this case, a new type of nonreciprocity is observed (namely, the relation R(α) ≠ R(–α) holds, where R is the reflection coefficient and α is the angle of incidence). It has been demonstrated that in the case of oblique incidence, there appears a new photonic forbidden band that is not selective relative to the polarization of incident light. We have detected strong dependences of reflectance, absorbance, transmittance nonreciprocity, and other characteristics on the angle between the direction of the external static magnetic field and the normal to the layer boundary. Such a system can be used as a controllable polarization filter and a mirror, as well as a source of circular (elliptic) polarization, a controllable optical diode, and so on.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamical Friction and the Evolution of Supermassive Black Hole Binaries: The Final Hundred-parsec Problem

The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes “hard” and eventually reaches coalescence through gravitational-wave emission. We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole. In our treatment, we include the frictional force from stars moving faster than the inspiralling object, which is neglected in the standard Chandrasekhar treatment. We show that the binary eccentricity increases if the stellar cusp density profile rises less steeply than ρ∝r{sup −2}. In cusps shallower than ρ∝r{sup −1}, the frictional timescale can become very long due to the deficit of stars moving slower than the massive body. Although including fast stars increases the decay rate, low mass-ratio binaries (q≲10{sup −3}) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers, the secondary hole stalls on an eccentric orbit at a distance of order one-tenth the influence radius of the primary hole (i.e., ≈10--100 pc for massive ellipticals). We calculate the expected number of stalled satellites as a function of the host galaxy mass and show that the brightest cluster galaxies should have ≳1 of such satellites orbiting within their cores. Our results could provide an explanation for a number of observations, which include multiple nuclei in core ellipticals, off-center AGNs, and eccentric nuclear disks.

79 ASTRONOMY AND ASTROPHYSICS↗

Stress-intensity factor calculations using the boundary force method

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.

Tan, P. W.↗

DUKSUP: A Computer Program for High Thrust Launch Vehicle Trajectory Design and Optimization

From the late 1960s through 1997, the leadership of NASAs Intermediate and Large class unmanned expendable launch vehicle projects resided at the NASA Lewis (now Glenn) Research Center (LeRC). One of LeRCs primary responsibilities --- trajectory design and performance analysis --- was accomplished by an internally-developed analytic three dimensional computer program called DUKSUP. Because of its Calculus of Variations-based optimization routine, this code was generally more capable of finding optimal solutions than its contemporaries. A derivation of optimal control using the Calculus of Variations is summarized including transversality, intermediate, and final conditions. The two point boundary value problem is explained. A brief summary of the codes operation is provided, including iteration via the Newton-Raphson scheme and integration of variational and motion equations via a 4th order Runge-Kutta scheme. Main subroutines are discussed. The history of the LeRC trajectory design efforts in the early 1960s is explained within the context of supporting the Centaur upper stage program. How the code was constructed based on the operation of the AtlasCentaur launch vehicle, the limits of the computers of that era, the limits of the computer programming languages, and the missions it supported are discussed. The vehicles DUKSUP supported (AtlasCentaur, TitanCentaur, and ShuttleCentaur) are briefly described. The types of missions, including Earth orbital and interplanetary, are described. The roles of flight constraints and their impact on launch operations are detailed (such as jettisoning hardware on heating, Range Safety, ground station tracking, and elliptical parking orbits). The computer main frames on which the code was hosted are described. The applications of the code are detailed, including independent check of contractor analysis, benchmarking, leading edge analysis, and vehicle performance improvement assessments. Several of DUKSUPs many major impacts on launches are discussed including Intelsat, Voyager, Pioneer Venus, HEAO, Galileo, and Cassini.

Launch vehicle performance optimization↗

Solving Critical Problems of the Muon Collider Higgs Factory: Optics, Magnets and their Protection, Detector Backgrounds

A low-energy medium-luminosity Muon Collider (MC) is being studied as a possible Higgs Factory (HF). Electrons from muon decays will deposit more than 300 kW in superconducting magnets of the HF collider ring. This imposes significant challenges to superconducting (SC) magnets used in the MC storage ring (SR) and interaction regions (IR). Magnet designs are proposed which provide high operating gradient and magnetic field in a large aperture to accommodate the large size of muon beams (due to low beta*), as well as a cooling system to intercept the large heat deposition from the showers induced by decay electrons. The distribution of heat deposition in the MC SR lattice elements requires large-aperture magnets in order to accommodate thick high-Z absorbers to protect the SC coils. Based on the developed MARS15 model and intensive simulations, a sophisticated radiation protection system was designed for the collider SR and IR to bring the peak power density in the superconducting coils below the quench limit and reduce the dynamic heat deposition in the cold mass by a factor of 100. The system consists of tight tungsten masks in the magnet interconnect regions and elliptical tungsten liners in the magnet aperture optimized individually for each magnet. These also reduce the background particle fluxes in the collider detector.

43 PARTICLE ACCELERATORS↗

Generation of circularly polarized XUV and soft-x-ray high-order harmonics by homonuclear and heteronuclear diatomic molecules subject to bichromatic counter-rotating circularly polarized intense laser fields

Recently, studies of bright circularly polarized high-harmonic beams from atoms in the soft-x-ray region as a source for x-ray magnetic circular dichroism measurement in a tabletop-scale setup have received considerable attention. In this paper, we address the problem with molecular targets and perform a detailed quantum study of H 2 +, CO, and N 2 molecules in bichromatic counter-rotating circularly polarized laser fields where we adopt wavelengths (1300 and 790 nm) and intensities (2 × 10 14 W/cm 2 ) reported in a recent experiment [Proc. Natl. Acad. Sci. USA 112, 14206 (2015)]. Our treatment of multiphoton processes in homonuclear and heteronuclear diatomic molecules is nonperturbative and based on the time-dependent density-functional theory for multielectron systems. The calculated radiation spectrum contains doublets of left and right circularly polarized harmonics with high-energy photons in the XUV and soft-x-ray ranges. Overall, our results reveal intriguing and substantially different nonlinear optical responses for homonuclear and heteronuclear diatomic molecules subject to circularly polarized intense laser fields. We study in detail the below- and above-threshold harmonic regions and analyze the ellipticity and phase of the generated harmonic peaks.

74 ATOMIC AND MOLECULAR PHYSICS↗

DUKSUP: A Computer Program for High Thrust Launch Vehicle Trajectory Design and Optimization

From the late 1960's through 1997, the leadership of NASA's Intermediate and Large class unmanned expendable launch vehicle projects resided at the NASA Lewis (now Glenn) Research Center (LeRC). One of LeRC's primary responsibilities --- trajectory design and performance analysis --- was accomplished by an internally-developed analytic three dimensional computer program called DUKSUP. Because of its Calculus of Variations-based optimization routine, this code was generally more capable of finding optimal solutions than its contemporaries. A derivation of optimal control using the Calculus of Variations is summarized including transversality, intermediate, and final conditions. The two point boundary value problem is explained. A brief summary of the code's operation is provided, including iteration via the Newton-Raphson scheme and integration of variational and motion equations via a 4th order Runge-Kutta scheme. Main subroutines are discussed. The history of the LeRC trajectory design efforts in the early 1960's is explained within the context of supporting the Centaur upper stage program. How the code was constructed based on the operation of the Atlas/Centaur launch vehicle, the limits of the computers of that era, the limits of the computer programming languages, and the missions it supported are discussed. The vehicles DUKSUP supported (Atlas/Centaur, Titan/Centaur, and Shuttle/Centaur) are briefly described. The types of missions, including Earth orbital and interplanetary, are described. The roles of flight constraints and their impact on launch operations are detailed (such as jettisoning hardware on heating, Range Safety, ground station tracking, and elliptical parking orbits). The computer main frames on which the code was hosted are described. The applications of the code are detailed, including independent check of contractor analysis, benchmarking, leading edge analysis, and vehicle performance improvement assessments. Several of DUKSUP's many major impacts on launches are discussed including Intelsat, Voyager, Pioneer Venus, HEAO, Galileo, and Cassini.

high thrust trajectory design↗

GPS World, Innovation: Autonomous Navigation at High Earth Orbits

Calculating a spacecraft's precise location at high orbital altitudes-22,000 miles (35,800 km) and beyond-is an important and challenging problem. New and exciting opportunities become possible if satellites are able to autonomously determine their own orbits. First, the repetitive task of periodically collecting range measurements from terrestrial antennas to high altitude spacecraft becomes less important-this lessens competition for control facilities and saves money by reducing operational costs. Also, autonomous navigation at high orbital altitudes introduces the possibility of autonomous station keeping. For example, if a geostationary satellite begins to drift outside of its designated slot it can make orbit adjustments without requiring commands from the ground. Finally, precise onboard orbit determination opens the door to satellites flying in formation-an emerging concept for many scientific space applications. The realization of these benefits is not a trivial task. While the navigation signals broadcast by GPS satellites are well suited for orbit and attitude determination at lower altitudes, acquiring and using these signals at geostationary (GEO) and highly elliptical orbits is much more difficult. The light blue trace describes the GPS orbit at approximately 12,550 miles (20,200 km) altitude. GPS satellites were designed to provide navigation signals to terrestrial users-consequently the antenna array points directly toward the earth. GEO and HE0 orbits, however, are well above the operational GPS constellation, making signal reception at these altitudes more challenging. The nominal beamwidth of a Block II/IIA GPS satellite antenna array is approximately 42.6 degrees. At GEO and HE0 altitudes, most of these primary beam transmissions are blocked by the Earth, leaving only a narrow region of nominal signal visibility near opposing limbs of the earth. This region is highlighted in gray. If GPS receivers at GEO and HE0 orbits were designed to use these higher power signals only, precise orbit determination would not be practical. Fortunately, the GPS satellite antenna array also produces side lobe signals at much lower power levels. NASA has designed and tested the Navigator, a new GPS receiver that can acquire and track these weaker signals, thereby dramatically increasing the signal visibility at these altitudes. While using much weaker signals is a fundamental requirement for a high orbital altitude GPS receiver, it is certainly not the only challenge. There are other unique characteristics of this application that must also be considered. For example, Position Dilution of Precision (PDOP) figures are much higher at GEO and HE0 altitudes because visible GPS satellites are concentrated in a much smaller area with respect to the spacecraft antenna. These poor PDOP values contribute considerable error to the point solutions calculated by the spacecraft GPS receiver. Finally, spacecraft GPS receivers must be designed to withstand a variety of extreme environmental conditions. Variations in acceleration between launch and booster separation are extreme. Temperature gradients in the space environment are also severe. Furthermore, radiation effects are a major concern-spacecraft-borne GPS receivers must be designed with radiation-hardened electronics to guard against this phenomenon, otherwise they simply will not work. Perhaps most importantly, there are no opportunities to repair or modify any space-borne GPS receiver after it has been launched. Great care must be taken to ensure all performance characteristics have been analyzed prior to liftoff.

Bamford, William↗

Flow Field Measurement of Mixing Driven by Buoyancy

Mixing driven by buoyancy-induced flows inside a cavity consists of stretching and folding of an interface. Measurement of the flow field using particle imaging velocimetry shows that during stretching the flow field has a single elliptic point, thus dominated by a single vortex. However, global bifurcation that results in folding introduces a hyperbolic point whereby the flow field degenerates to multiple vortex interactions. The short-lived coherent structure observed during mixing which results in the Rayleigh- Taylor morphology is attributed to vortex interactions. The mixing characteristics of non-homogeneous fluids driven by buoyancy are important towards understanding transport phenomenon in a microgravity environment. Mixing consists of stretching and folding of an interface due to a flow field whose intensity depends on the body force. For miscible liquids, the characteristic of the flow field determines whether mass transport is governed by diffusion or bulk stirring which induces mixing. For technologically important processes, transport of mass is governed by the coupling of the body force to scalar gradients such as concentration and or temperature' 2 3 . In order to lend insight into these classes of problems we consider a model experimental system to study mixing driven by buoyancy-induced flows. The characteristics of mixing is addressed from detail measurements of the flow field using particle imaging velocimetry (PIV), and its corresponding interface dynamics using image processing techniques.

Batur, C.↗

Probing the tides in interacting galaxy pairs

Detailed spectroscopic and imaging observations of colliding elliptical galaxies revealed unmistakable diagnostic signatures of the tidal interactions. It is possible to compare both the distorted luminosity distributions and the disturbed internal rotation profiles with numerical simulations in order to model the strength of the tidal gravitational field acting within a given pair of galaxies. Using the best-fit numerical model, one can then measure directly the mass of a specific interacting binary system. This technique applies to individual pairs and therefore complements the classical methods of measuring the masses of galaxy pairs in well-defined statistical samples. The 'personalized' modeling of galaxy pairs also permits the derivation of each binary's orbit, spatial orientation, and interaction timescale. Similarly, one can probe the tides in less-detailed observations of disturbed galaxies in order to estimate some of the physical parameters for larger samples of interacting galaxy pairs. These parameters are useful inputs to the more universal problems of (1) the galaxy merger rate, (2) the strength and duration of the driving forces behind tidally stimulated phenomena (e.g., starbursts and maybe quasi steller objects), and (3) the identification of long-lived signatures of interaction/merger events.

Borne, Kirk D.↗

A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier–Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.

Computer Science↗