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NASA NTRS1993

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

Bates, J. R.↗

NASA NTRS1993

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Moorthi, Shrinivas↗

NASA NTRS1993

Investigation of high-speed free shear flows using improved pressure-strain correlated Reynolds stress turbulence model

A high-speed shear layer is studied using compressibility corrected Reynolds stress turbulence model which employs newly developed model for pressure-strain correlation. MacCormack explicit prediction-corrector method is used for solving the governing equations and the turbulence transport equations. The stiffness arising due to source terms in the turbulence equations is handled by a semi-implicit numerical technique. Results obtained using the new model show a sharper reduction in growth rate with increasing convective Mach number. Some improvements were also noted in the prediction of the normalized streamwise stress and Reynolds shear stress. The computed results are in good agreement with the experimental data.

Tiwari, S. N.↗

NASA NTRS1993

Numerical simulation of steady and unsteady viscous flow in turbomachinery using pressure based algorithm

The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake. The predicted unsteady wake profiles are compared with the available experimental data and the agreement is good. The numerical results are interpreted to draw conclusions on the unsteady wake transport mechanism in the blade passage.

Lakshminarayana, B.↗

NASA NTRS1995

On the Conservative Interface Treatment for Multi-Block Viscous Flow Computations

A pressure-based multi-block computational method is developed for solving the incompressible Navier-Stokes equations in general curvilinear grid systems. The scheme is based on the semi-implicit type flow solver with the staggered grid. Issues concerning the mass and momentum flux treatments at the discontinuous grid interface are addressed. Systematic numerical experiments for different interface treatments involving (1) straightforward interpolation, (2) globally conservative scheme, and (3) locally conservative scheme have been conducted. It is demonstrated that mass conservation has to be maintained locally, at the grid interface, with accuracy compatible with that of the scheme used in interior domain. Direct interpolation or globally conservative interface treatment of mass flux can not yield solutions with desirable accuracy.

Liu, J.↗

NASA NTRS1993

A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles

Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined Eulerian-Lagrangian technique, in which Eulerian conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.

Dejong, Frederik J.↗

NASA NTRS1994

Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

Balachandar, S.↗

NASA NTRS1995

Diabatic forcing and intialization with assimilation of cloud water and rainwater in a forecast model

In this study, diabatic forcing, and liquid water assimilation techniques are tested in a semi-implicit hydrostatic regional forecast model containing explicit representations of grid-scale cloud water and rainwater. Diabatic forcing, in conjunction with diabatic contributions in the initialization, is found to help the forecast retain the diabatic signal found in the liquid water or heating rate data, consequently reducing the spinup time associated with grid-scale precipitation processes. Both observational Special Sensor Microwave/Imager (SSM/I) and model-generated data are used. A physical retrieval method incorporating SSM/I radiance data is utilized to estimate the 3D distribution of precipitating storms. In the retrieval method the relationship between precipitation distributions and upwelling microwave radiances is parameterized, based upon cloud ensemble-radiative model simulations. Regression formulae relating vertically integrated liquid and ice-phase precipitation amounts to latent heating rates are also derived from the cloud ensemble simulations. Thus, retrieved SSM/I precipitation structures can be used in conjunction with the regression-formulas to infer the 3D distribution of latent heating rates. These heating rates are used directly in the forecast model to help initiate Tropical Storm Emily (21 September 1987). The 14-h forecast of Emily's development yields atmospheric precipitation water contents that compare favorably with coincident SSM/I estimates.

Raymond, William H.↗

NASA NTRS1989

Low gravity transfer line chilldown

A code has been developed that solves for the transfer line chilldown time and flow and heat transfer characteristics in one-g environment. The code solves the transient, one dimensional, space averaged mass, momentum, and energy conservation equations for liquid-vapor two-phase flow in tubes. The physical configuration solved is that appropriate for bottom coolant injection in a vertically supported heated tube. Four distinct regions are considered consecutively: fully liquid, inverted annular, dispersed, and fully vapor flow. The conservation equations for both the liquid and the vapor are solved in each region separately. Also, in each region the mass and energy transport between each phase as well as the energy and momentum transport between the tube wall and the fluid are accounted for. A finite wall thickness is also considered. The model described above was solved numerically through a mixed finite difference scheme with forward time marching. The inverted annular regime was resolved using a semi-implicit finite differencing while the dispersed regime was solved explicitly. Also, a staggered mesh was used in which the velocity was resolved at mesh boundaries while all other field variables were resolved at the mesh centroids. Different mesh sizes were used depending on the region of solution. A coarse mesh was used in the dispersed flow region while a much finer mesh was used in both the inverted annular flow region and the tube walls.

B. N. Antar↗

NASA NTRS1998

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

VanOverbeke, Thomas J.↗

NASA NTRS1999

Development of a Multi-Disciplinary Computing Environment (MDICE)

The growing need for and importance of multi-component and multi-disciplinary engineering analysis has been understood for many years. For many applications, loose (or semi-implicit) coupling is optimal, and allows the use of various legacy codes without requiring major modifications. For this purpose, CFDRC and NASA LeRC have developed a computational environment to enable coupling between various flow analysis codes at several levels of fidelity. This has been referred to as the Visual Computing Environment (VCE), and is being successfully applied to the analysis of several aircraft engine components. Recently, CFDRC and AFRL/VAAC (WL) have extended the framework and scope of VCE to enable complex multi-disciplinary simulations. The chosen initial focus is on aeroelastic aircraft applications. The developed software is referred to as MDICE-AE, an extensible system suitable for integration of several engineering analysis disciplines. This paper describes the methodology, basic architecture, chosen software technologies, salient library modules, and the current status of and plans for MDICE. A fluid-structure interaction application is described in a separate companion paper.

Kingsley, Gerry↗

NASA NTRS2000

Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme

The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi-Lagrangian dynamics employed in the MACCM3. This type of dynamical core (employed with a 60-min time step) is likely to reduce SLT's interpolation errors that are compounded by the short-term variability characteristic of the explicit centered-difference dynamics employed in the SKYHI model (time step of 3 min). In the extreme case of a very slowly varying circulation, the choice of advection scheme has no effect on two-dimensional (latitude-height) age-of-air calculations, owing to the smooth nature of the transport circulation in 2D models. These results suggest that nondiffusive schemes may be the preferred choice for multiyear simulations of tracers not overly sensitive to the requirement of monotonicity (this category includes many greenhouse gases). At the same time, age-of-air calculations offer a simple quantitative diagnostic of a scheme's long-term diffusive properties and may help in the evaluation of dynamical cores in multiyear integrations. On the other hand, the sensitivity of the computed ages to the model numerics calls for caution in using age of air as a diagnostic of a GCM's large-scale circulation field.

Eluszkiewicz, Janusz↗

NASA NTRS2001

Studies of Plasma Flow Past Jupiter's Galilean Satellites

We have investigated the interaction of Io, Jupiter's innermost Galilean satellite, with the Io plasma torus, using our semi-implicit time-dependent 3D MHD code to model the plasma interactions. We have used the same code to model the plasma interaction at Ganymede.

Linker, Jon A.↗

NASA NTRS2006

Fibonacci Grids

Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.

Swinbank, Richard↗

NASA NTRS2010

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗

NASA NTRS2014

Physics Based Model for Cryogenic Chilldown and Loading. Part I: Algorithm

We report the progress in the development of the physics based model for cryogenic chilldown and loading. The chilldown and loading is model as fully separated non-equilibrium two-phase flow of cryogenic fluid thermally coupled to the pipe walls. The solution follow closely nearly-implicit and semi-implicit algorithms developed for autonomous control of thermal-hydraulic systems developed by Idaho National Laboratory. A special attention is paid to the treatment of instabilities. The model is applied to the analysis of chilldown in rapid loading system developed at NASA-Kennedy Space Center. The nontrivial characteristic feature of the analyzed chilldown regime is its active control by dump valves. The numerical predictions are in reasonable agreement with the experimental time traces. The obtained results pave the way to the development of autonomous loading operation on the ground and space.

heat transfer↗

DOE OSTI2022

Extension of the high-resolution thermal-hydraulics code ESCOT to hexagonal core geometries for multi-physics calculations

The extension of the capabilities of the pin-level nuclear reactor core thermal-hydraulics (T/H) code ESCOT to analyze hexagonal fueled cores and its performance are presented. ESCOT is an accurate yet fast core thermal-hydraulics solution aiming at high-fidelity and high-resolution multi-physics core analysis in the framework of massively parallel computing platforms. Its algorithm solution is based on the four-equation drift-flux model for two-phase calculations, these are numerically solved by applying the Finite Volume Method (FVM) and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE)-like algorithm in a staggered grid system. Constitutive models such as turbulent mixing, pressure drop, and vapor generation are employed to simulate key phenomena in subchannel-scale analysis. ESCOT is parallelized by a double (radial and axial) domain decomposition that enables its highly parallelized execution. The coupling of the code with the neutronics whole core solver for hexagonal geometries nTRACER is described. The newly implemented ESCOT features are validated by comparing single assembly and full core steady state nTRACER-ESCOT solutions with nTRACER standalone internal one-dimensional T/H solver results. The validation problems are based on the VVER 440 and VVER 1000 cores. ESCOT results show differences within an acceptable range with respect to the simple 1D nTRACER built-in solver. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗