Results for “Mode Solver” — Page 19

DOE OSTI2022

Global gyrokinetic simulations of ASDEX Upgrade up to the transport timescale with GENE–Tango

An accurate description of turbulence up to the transport timescale is essential for predicting core plasma profiles and enabling reliable calculations for designing advanced scenarios and future devices. Here, we exploit the gap separation between turbulence and transport timescales and couple the global gyrokinetic code GENE to the transport-solver Tango, including kinetic electrons, collisions, realistic geometries, toroidal rotation and electromagnetic effects for the first time. This approach overcomes gyrokinetic codes' limitations and enables high-fidelity profile calculations in experimentally relevant plasma conditions, significantly reducing the computational cost. We present numerical results of GENE–Tango for two ASDEX Upgrade discharges, one of which exhibits a pronounced peaking of the ion temperature profile not reproduced by TGLF–ASTRA. We show that GENE–Tango can correctly capture the ion temperature peaking observed in the experiment. By retaining different physical effects in the GENE simulations, e.g., collisions, toroidal rotation and electromagnetic effects, we show that the ion temperature profile's peaking can be linked to electromagnetic effects of submarginal (stable) KBM modes. Furthermore, based on these results, the expected GENE–Tango speedup for the ITER standard scenario is larger than two orders of magnitude compared to a single gyrokinetic simulation up to the transport timescale, possibly making first-principles ITER simulations feasible on current computing resources.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

Dynamic Aeroelastic Flight Dynamic Modeling of Mach 0.745 Transonic Truss-Braced Wing

This paper presents a modeling approach for dynamic aeroelastic flight dynamic analysis of the Mach0.745 Transonic Truss-Braced Wing. The modeling approach is based on a transonic correction method to correct the Theodorsen’s theory for transonic flow. CFD unsteady Reynolds-averaged Navier-Stokes equations (RANS) simulations are conducted using FUN3D solver for a series of wing sections from the Mach 0.745Transonic Truss-Braced Wing in pitch and plunge oscillations. Unsteady lift and pitching moment coefficients are obtained and used to develop the correction terms in the Theodorsen’s theory to account for transonic aerodynamics. The unsteady lift and pitching moment derivatives with respect to the unsteady angle of attack are obtained as functions of the reduced frequency. These derivatives are used to compute the unsteady lift and pitching moment contributions by the angle of attack, pitch rate, and roll rate. They are then approximated using a frequency-domain regression to obtain the dynamic stability derivatives for the Mach 0.745 Transonic Truss-Braced Wing. The structural dynamic mode shapes of the Mach 0.745 TTBW are extracted from a NAS-TRAN finite-element model. These mode shapes are used to compute the generalized unsteady aerodynamic forces. The aerodynamic mass, damping, and stiffness and the aerodynamic lag states are constructed to couple the dynamic aeroelastic contribution to the flight dynamic model of the Mach 0.745 Transonic Truss-Braced Wing. The coupled dynamic aeroelastic flight dynamic equations of motion are formulated. The eigenvalues of the coupled system are computed. All the flight dynamic modes and structural dynamic modes are stable at Match 0.745. The effect of transonic aerodynamics generally causes all the dynamic modes to have lower damping values

Flight Dynamics↗

NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗

DOE OSTI2015

Partnership for Edge Physics Simulation (EPSI)

We propose to develop advanced simulation codes, based upon an extreme parallelism, first principles kinetic approach, to address the challenges associated with the edge region of magnetically confined plasmas. This work is relevant to both existing magnetic fusion facilities and essential for next-generation burning plasma experiments, such as ITER where success is critically dependent upon H-mode operation achieving an edge pedestal of sufficient height for good core plasma performance without producing deleterious large scale edge localized instabilities. The plasma edge presents a well-known set of multi-physics, multi-scale problems involving complex 3D magnetic geometry. Perhaps the greatest computational challenge is the lack of scale separation – temporal scales for drift waves, Alfven waves, ELM dynamics for example have strong overlap. Similar overlap occurs on the spatial scales for the ion poloidal gyro-radius, drift wave and pedestal width. The traditional approach of separating fusion problems into weakly interacting spatial or temporal domains clearly breaks down in the edge. A full kinetic model (full-f model) must be solved to understand and predict the edge physics including non-equilibrium thermodynamic issues arising from the magnetic topology (the open field lines producing a spatially sensitive velocity hole), plasma wall interactions, neutral and atomic physics. The plan here is to model these phenomena within a comprehensive first principles set of equations without the need for the insurmountable multiple-codes coupling issues by building on the XGC1 code developed under the SciDAC Proto-FSP Center for Plasma Edge Simulation (CPES). This proposal includes the critical participants in the XGC1 development. We propose enhancing the capability of XGC1 by including all the important turbulence physics contained in kinetic ion and electron electromagnetic dynamics, by extending the PIC technology to incorporate several positive features found in the Eulerian grid technology, combining the coarse grained XGC0 code into it with a multiscale projective time integration technique to be developed in the project for experimental time scale simulation of the edge multi-physics, and by implementing modern computational technologies to move forward with the extreme scale heterogeneous hardware/software platform development. Ultra-fast edge localized instabilities, involving compressional Alven modes, will be studied using a proper MHD or two-fluid codes employing kinetic closure information from XGC. The proposed research integrates the most important physical processes on overlapping temporal and spatial scales, to study (i) transitions and thresholds for enhanced confinement regimes, (ii) the predictive understanding of the edge pedestal formation, structure and dynamics, (iii) the effect of the edge plasma on the core confinement, (iv) the physics of Edge Localized Modes and their suppression or mitigation via external control techniques, and (v) the heat load on the material wall. Our approach will implement physical models that are valid in their relevant collisionality regimes for current experiments and future burning plasma devices. Comparisons with experimental data will be made at multiple levels including characterization of turbulence dynamics, flux-gradient responses in the energy, particle and momentum channels, and observations of global phenomena such as L-H transitions, momentum generation, ELM dynamics, ELM-free regimes and the tokamak density limit. The proposal team has established strong connections, through joint membership, with other organizations that will be critical for success. These include FASTMath, SUPER and QUEST Institutes respectively for meshing tools and solvers; code performance tuning and uncertainty quantification as well as a proposed Data Management and Visualization Institute.. We will also be teaming with ongoing fusion SciDAC’s: CSWPI for RF-edge plasmas interactions; CEMM for the M3D MHD simulations and with PEPSC for incorporation of energetic particle physics. Finally, the team includes representatives from each of the major U.S. experimental facilities who will coordinate the validation program and the development of synthetic diagnostics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Development of a continuous synthesis process for carbamazepine using validated in-line Raman spectroscopy and kinetic modelling for disturbance simulation

Mitigation of failure modes in the continuous synthesis (CS) of a drug substance (DS) has the potential to widen the adoption of continuous manufacturing (CM) technologies by the pharmaceutical industry. Here, this work demonstrates the development of a robust continuous process for the synthesis of carbamazepine (CBZ), an essential medicine as per the World Health Organization (WHO), facilitated by kinetic modelling and monitored by in-line Raman spectroscopy. Accurate kinetic modelling and the use of validated process analytical technology (PAT) models for quantitative measurement were found to play an important role in developing CS of drug substances. Kinetic data for the formation of CBZ from iminostilbene (ISB) were collected by batch reaction sampling and high-performance liquid chromatography (HPLC) analysis. A non-linear solver and iterative method was applied to determine two sets of Arrhenius parameters simultaneously for the reaction system by minimizing the standard error of the model fit. The start-up and dynamic equilibrium stages for the CS of CBZ using a continuous stirred tank reactor (CSTR) were modelled based on the batch kinetic data and employed to optimize conversion and simulate process disturbances. An in-line Raman spectroscopy method was successfully developed, validated, and integrated to determine the concentrations of CBZ and ISB within the operating range for the CS. The CS kinetic model was evaluated experimentally from startup to dynamic equilibrium over 10 residence times with monitoring by HPLC and in-line Raman spectroscopy. The developed kinetic model in tandem with in-line Raman spectroscopy successfully predicted disturbances due to changes in process variables and can serve as a useful tool in the future design of advanced process control strategies for the continuous synthesis of CBZ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Separation and Transition on the ROTEX-T Cone-Flare

As part of NATO STO AVT-346 “Predicting Hypersonic Boundary-Layer Transition on Complex Geometries,” coordinated experimental and computational studies were conducted on the ROTEX-T, a cone-flare geometry used in a successful flight-test experiment. At the as-flown conditions, a separation bubble existed at the compression corner. Separation, reattachment, and the multifaceted linear instability paths leading this bubble to transition to turbulence are challenging to predict, but have significant impact on surface pressure and heat flux. High-resolution background-oriented schlieren and infrared thermography measurements were made in the AFOSR–Notre Dame Large Mach-6 Quiet Tunnel at freestream unit Reynolds numbers from 5.8×10(exp 6) to 12.2×10(exp 6) m-1and nominally zero angle of attack. High-speed self-aligned focusing schlieren, infrared thermography, and focused laser differential interferometry measurements were made in the AFRL Mach-6 Ludwieg Tube from 2.2×10(exp 6) to 24.7×10(exp 6) m-1and nominally zero degrees angle of attack. The surface heat-flux and Stanton number distributions were computed. Separation and reattachment locations, as well as the flow state at each, were determined from the combination of surface and off-wall measurements. The convective and global boundary-layer instabilities of the axisymmetric laminar flow at the experimental conditions were investigated computationally. Amplification of Mack’s first and second modes were observed to have logarithmic amplification factors between 5 to 7.5 at the separation location, depending on conditions. The flow was found to be globally unstable to stationary three-dimensional disturbances concentrated in the reattachment region. Previous analysis of the ROTEX-T flight data had not assessed reattachment location or the flow state upon reattachment. Thanks to the insights gained from the coordinated, on- and off-wall ground-test measurements, these evaluations have now been made. The separation location indicated by laminar simulations is consistently numerically predicted to be upstream of the experimentally observed location for a transitional separation bubble. The cause of this difference is understood to lie in the steady-state and axisymmetric assumptions made by both solvers employed to compute the basic states analyzed, as flow topology considerations assert that unsteady two-dimensional or axisymmetric separation bubbles are structurally unstable and will become three-dimensional. Computed laminar heating rates prior to separation agreed well with experiment; transitional heating rates after reattachment were between laminar and turbulent computations.

CFD Validation↗

NASA NTRSDate not supplied

Separation and Transition on the ROTEX-T Cone-Flare

As part of NATO STO AVT-346 “Predicting Hypersonic Boundary-Layer Transition on Complex Geometries,” coordinated experimental and computational studies were conducted on the ROTEX-T, a cone-flare geometry used in a successful flight-test experiment. At the as-flown conditions, a separation bubble existed at the compression corner. Separation, reattachment, and the multifaceted linear instability paths leading this bubble to transition to turbulence are challenging to predict, but have significant impact on surface pressure and heat flux. High-resolution background-oriented schlieren and infrared thermography measurements were made in the AFOSR–Notre Dame Large Mach-6 Quiet Tunnel at freestream unit Reynolds numbers from 5.8×10(exp 6) to 12.2×10(exp 6) m-1and nominally zero angle of attack. High-speed self-aligned focusing schlieren, infrared thermography, and focused laser differential interferometry measurements were made in the AFRL Mach-6 Ludwieg Tube from 2.2×10(exp 6) to 24.7×10(exp 6) m-1and nominally zero degrees angle of attack. The surface heat-flux and Stanton number distributions were computed. Separation and reattachment locations, as well as the flow state at each, were determined from the combination of surface and off-wall measurements. The convective and global boundary-layer instabilities of the axisymmetric laminar flow at the experimental conditions were investigated computationally. Amplification of Mack’s first and second modes were observed to have logarithmic amplification factors between 5 to 7.5 at the separation location, depending on conditions. The flow was found to be globally unstable to stationary three-dimensional disturbances concentrated in the reattachment region. Previous analysis of the ROTEX-T flight data had not assessed reattachment location or the flow state upon reattachment. Thanks to the insights gained from the coordinated, on- and off-wall ground-test measurements, these evaluations have now been made. The separation location indicated by laminar simulations is consistently numerically predicted to be upstream of the experimentally observed location for a transitional separation bubble. The cause of this difference is understood to lie in the steady-state and axisymmetric assumptions made by both solvers employed to compute the basic states analyzed, as flow topology considerations assert that unsteady two-dimensional or axisymmetric separation bubbles are structurally unstable and will become three-dimensional. Computed laminar heating rates prior to separation agreed well with experiment; transitional heating rates after reattachment were between laminar and turbulent computations.

CFD Validation↗

DOE OSTI2018

Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,v r ,v θ ) phase space coordinates

In this paper, a fourth-order finite-volume Vlasov–Poisson algorithm is developed for simulating axisymmetric plasma configurations in ( r , v r , v θ ) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order upwind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. Finally, the finite-volume implementation is demonstrated to converge at fourth-order for both applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas

Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literature AB that is appropriate for such studies. In particular, the formulation uses a set of time-dependent drift-kinetic equations (DKEs) to advance the non-Maxwellian part of the electron and ion distribution functions ( fNM ) with linearized Fokker-Planck-Landau collision operators. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that fNM carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by a set of MHD equations which are closed by moments of fNM . We then present two DKE solvers based upon this formulation in axisymmetric toroidal geometries. The Neoclassical Ion-Electron Solver (NIES) solves the steady-state DKEs in the low-collisionality limit. Convergence and benchmark studies are discussed, providing a proof-of-principle that this new formulation can accurately reproduce results from the literature in the limit considered. We then present the DK4D code which evolves the finite-collisionality DKEs time-dependently. Computational methods used and successful benchmarks to other neoclassical models and codes are discussed. Furthermore, we couple DK4D to a reduced, transport-timescale MHD code. The resulting hybrid code is used to simulate the evolution of the current density in a large-aspect-ratio plasma in the presence of several different time-dependent pressure profiles. These simulations demonstrate the self-consistent, dynamic formation of the ohmic and bootstrap currents. In the slowly-evolving plasmas considered, these first-principle simulations are shown to verify a simpler, steady-state neoclassical model that is commonly used in transport codes. Future work will involve coupling DK4D to a spatially three-dimensional, extended MHD code, generalizing DK4D to nonaxisymmetric geometries, and simulating more quickly-evolving and realistic plasmas. The ultimate goal of this work is to perform self-consistent, hybrid simulations of complex tokamak instabilities and calculations of neoclassical toroidal viscosity. A J. J. Ramos, Phys. Plasmas 17 , 082502 (2010). B J. J. Ramos, Phys. Plasmas 18 , 102506 (2011).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Feasibility of a multigroup Boltzmann–Fokker–Planck solution for electron beam dose calculations

Legacy nuclear-reactor Boltzmann solvers start clinical deployment as an alternative to Monte Carlo (MC) codes and Fermi–Eyges semiemprical models in radiation oncology treatment planning. Today’s certified clinical solvers are limited to photon beams. In this paper, ELECTR, a state-of-the-art multigroup electron cross sections generation module in NJOY is presented and validated against Lockwood’s calorimetric measurements, EGS-nrc and GEANT-4 for 1–20 MeV unidirectional electron beams. The nuclear-reactor DRAGON-5 solver is upgraded to access the library and solve the Boltzmann–Fokker–Planck (BFP) equation. A variety of heterogeneous radiotherapy and radiosurgery phantom configurations were used for validation purpose. Case studies include a thorax benchmark, that of a typical breast Intra-Operative Radiotherapy and a high-heterogeneity patient-like benchmark. For all beams, 100% of the water voxels satisfied the American Association of Physicists in Medicine accuracy criterion for a BFP-MC dose error below 2%. At least, 97.0% of adipose, muscle, bone, lung, tumor and breast voxels satisfied the 2% criterion. The average BFP-MC relative error was about 0.56% for all voxels, beams and materials combined. By irradiating homogeneous slabs from Z = 1 (hydrogen) to Z = 99 (einsteinium), we reported performance and defects of the CEPXS mode [US. Sandia National Lab., SAND-89-1685] in ELECTR for the entire periodic table. For all Lockwood’s benchmarks, NJOY-DRAGON dose predictions are within the experimental data precision for 98% of voxels.

42 ENGINEERING↗

NASA NTRS1991

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time marching Full Potential cascade solver are developed and verified. In the first method, the Influence Coefficient, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier Transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers.

Bakhle, Milind A.↗

NASA NTRS1991

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time marching Full Potential cascade solver are developed and verified. In the first method, the Influence Coefficient, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier Transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers.

Bakhle, M. A.↗

NASA NTRS2004

Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations

A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.

Reddy, Tondapu S.↗

NASA NTRS1991

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time-marching Full-Potential cascade solver are developed and verified. In the first method, the Influence Coefficient method, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response method, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers using both flat plates and actual airfoils.

Bakhle, Milind A.↗

NASA NTRS1998

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

Llorente, Ignacio M.↗

DOE OSTI2017

Simulations of Seismic Wave Propagation on Mars

In this paper, we present global and regional synthetic seismograms computed for 1D and 3D Mars models based on the spectral-element method. For global simulations, we implemented a radially-symmetric Mars model with a 110 km thick crust. For this 1D model, we successfully benchmarked the 3D seismic wave propagation solver SPECFEM3D_GLOBE against the 2D axisymmetric wave propagation solver AxiSEM at periods down to 10 s. We also present higher-resolution body-wave simulations with AxiSEM down to 1 s in a model with a more complex 1D crust, revealing wave propagation effects that would have been difficult to interpret based on ray theory. For 3D global simulations based on SPECFEM3D_GLOBE, we superimposed 3D crustal thickness variations capturing the distinct crustal dichotomy between Mars’ northern and southern hemispheres, as well as topography, ellipticity, gravity, and rotation. The global simulations clearly indicate that the 3D crust speeds up body waves compared to the reference 1D model, whereas it significantly changes surface waveforms and their dispersive character depending on its thickness. We also perform regional simulations with the solver SES3D based on 3D crustal models derived from surface composition, thereby addressing the effects of various distinct crustal features down to 2 s. The regional simulations confirm the strong effects of crustal variations on waveforms. Finally, we conclude that the numerical tools are ready for examining more scenarios, including various other seismic models and sources.

58 GEOSCIENCES↗

NASA NTRS1995

NAS Experiences of Porting CM Fortran Codes to HPF on IBM SP2 and SGI Power Challenge

Current Connection Machine (CM) Fortran codes developed for the CM-2 and the CM-5 represent an important class of parallel applications. Several users have employed CM Fortran codes in production mode on the CM-2 and the CM-5 for the last five to six years, constituting a heavy investment in terms of cost and time. With Thinking Machines Corporation's decision to withdraw from the hardware business and with the decommissioning of many CM-2 and CM-5 machines, the best way to protect the substantial investment in CM Fortran codes is to port the codes to High Performance Fortran (HPF) on highly parallel systems. HPF is very similar to CM Fortran and thus represents a natural transition. Conversion issues involved in porting CM Fortran codes on the CM-5 to HPF are presented. In particular, the differences between data distribution directives and the CM Fortran Utility Routines Library, as well as the equivalent functionality in the HPF Library are discussed. Several CM Fortran codes (Cannon algorithm for matrix-matrix multiplication, Linear solver Ax=b, 1-D convolution for 2-D datasets, Laplace's Equation solver, and Direct Simulation Monte Carlo (DSMC) codes have been ported to Subset HPF on the IBM SP2 and the SGI Power Challenge. Speedup ratios versus number of processors for the Linear solver and DSMC code are presented.

Saini, Subhash↗

DOE OSTI2016

A hybrid incremental projection method for thermal-hydraulics applications

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

97 MATHEMATICS AND COMPUTING↗