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NASA NTRS2000

A Finite-Element Approach for Modeling Inviscid and Viscous Compressible Flows using Prismatic Grids

The Galerkin finite-element method is used to solve the Euler and Navier-Stokes equations on prismatic meshes. It is shown that the prismatic grid is advantageous for correctly and efficiently capturing the boundary layers in high Reynolds number flows. It can be captured accurately because of the ability to cluster grid points normal to the body. The efficiency derives from the implicit treatment of the normal direction. To treat the normal direction implicitly, a semi-implicit Runge-Kutta time stepping scheme is developed. The semi-implicit algorithm is validated on simple geometries for inviscid and viscous flows and its convergence history is compared to that of the explicit Runge-Kutta scheme. The semi-implicit scheme is shown to be a factor of 3 to 4 faster in terms of CPU time to convergence.

Pandya, S. A.↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRS1980

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗

NASA NTRS1989

Evaluation of the heat transfer module (FAHT) of Failure Analysis Nonlinear Thermal And Structural Integrated Code (FANTASTIC)

The heat transfer module of FANTASTIC Code (FAHT) is studied and evaluated to the extend possible during the ten weeks duration of this project. A brief background of the previous studies is given and the governing equations as modeled in FAHT are discussed. FAHT's capabilities and limitations based on these equations and its coding methodology are explained in detail. It is established that with improper choice of element size and time step FAHT's temperature field prediction at some nodes will be below the initial condition. The source of this unrealistic temperature prediction is identified and a procedure is proposed for avoiding this phenomenon. It is further shown that the proposed procedure will converge to an accurate prediction upon mesh refinement. Unfortunately due to lack of time FAHT's ability to accurately account for pyrolysis and surface ablation has not been verified. Therefore, at the present time it can be stated with confidence that FAHT can accurately predict the temperature field for a transient multi-dimensional, orthotropic material with directional dependence, variable property, with nonlinear boundary condition. Such a prediction will provide an upper limit for the temperature field in an ablating decomposing nozzle liner. The pore pressure field, however, will not be known.

Keyhani, Majid↗

NASA NTRS1997

Magnetic Damping of g-Jitter Driven Flows: 3-D Calculations

A 3-D numerical model is developed to represent the oscillating natural convection induced in a cylindrical cavity filled with Ga-doped germanium with and without the presence of an external magnetic field. The model is developed based on the penalty-finite element solution of the equations describing the transport of momentum, heat and solutal element as well as the electromagnetic field distribution in the melt pool. Automatic time step control is applied to help speed up the calculations. Numerical simulations are conducted to study the convection and magnetic damping effects as a function of frequency, directions and amplitudes of g-jitter and also the direction and magnitudes of the applied magnetic fields. The results show that the g-jitter driven flow is time dependent and exhibits a complex recirculating convection pattern in three dimensions and that an applied magnetic field can be employed to suppress this deleterious convective flow and both magnitude and orientation of the applied field are important in magnetic damping of the g-jitter induced convective flows.

Shang, D. Y.↗

NASA NTRS2013

Developing an Accurate CFD Based Gust Model for the Truss Braced Wing Aircraft

The increased flexibility of long endurance aircraft having high aspect ratio wings necessitates attention to gust response and perhaps the incorporation of gust load alleviation. The design of civil transport aircraft with a strut or truss-braced high aspect ratio wing furthermore requires gust response analysis in the transonic cruise range. This requirement motivates the use of high fidelity nonlinear computational fluid dynamics (CFD) for gust response analysis. This paper presents the development of a CFD based gust model for the truss braced wing aircraft. A sharp-edged gust provides the gust system identification. The result of the system identification is several thousand time steps of instantaneous pressure coefficients over the entire vehicle. This data is filtered and downsampled to provide the snapshot data set from which a reduced order model is developed. A stochastic singular value decomposition algorithm is used to obtain a proper orthogonal decomposition (POD). The POD model is combined with a convolution integral to predict the time varying pressure coefficient distribution due to a novel gust profile. Finally the unsteady surface pressure response of the truss braced wing vehicle to a one-minus-cosine gust, simulated using the reduced order model, is compared with the full CFD.

Bartels, Robert E.↗

NASA NTRS1986

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Imlay, S. T.↗

NASA NTRSDate not supplied

Development of the GeoNEX Level 2G Products: Exploiting the Diurnal Variability of TOA Reflectance in Atmospheric Correction

This study develops a new atmospheric correction algorithm to generate the Level 2G products, in particular the gap-filled Surface Reflectance at 10-minute time steps, for the Geostationary-NASA Earth Exchange (GeoNEX) project. The algorithm is based on the MODIS MAIAC (Multi-Angle Implementation of Atmospheric Correction) framework but with significant modifications to exploit angular/temporal information from the diurnal variability of the GeoNEX L1G TOA (Top-of-Atmosphere) reflectance. The algorithm starts by evaluating the roughness/smoothness of the diurnal time series of the TOA reflectance. Because rapid changes in TOA reflectance are generally caused by passing clouds or shadows, rough segments of the time series are automatically filtered out while the smooth segments are further tested for brightness and temperature to identify clear-sky and snow-free observations. Next the algorithm runs the MAIAC RTM (Radiative Transfer Model) to retrieve the Ross-Thick-Li-Sparse (RTLS) BRDF model parameters and the daily-mean atmospheric optical depth (AOD) that allow the RTM to optimally simulate the observed diurnal variability of clear-sky TOA reflectance. Once the initial RTLS parameters are retrieved after the algorithm’s burn-in period, they are used as the prior information to predict the AOD level for the next days, while the subsequent clear-sky observations are used to make necessary adjustments to the RTLS parameters in an continuous fashion. This “prediction-analysis” cycle is then iterated to process the full time series of the L1G data, skipping only total-cloudy days or when surface snow is detected. We tested the algorithm over a list of selected AERONET sites. The retrieved results (the daily mean AOD and the RTLS parameters) reasonably agree with the ground-based measurements. Importantly, the results indicate that the diurnal cycles of surface reflectance are continuous functions of the illumination-view geometry. Thus we can use the retrieved RTLS model to accurately fill in data gaps on partial cloudy days. Also, our algorithm is totally independent from the traditional approaches based on the use of spectral band ratios between the shortwave infrared (e.g., 2.2µm) and the visible (e.g., 0.47µm and 0.64µm) bands. Our results thus demonstrate that the high-frequent diurnal geostationary observations contain unique information that helps us improve atmospheric correction of remote sensing data.

GeoNEX↗

NASA NTRS1982

Ageostrophic winds in the severe strom environment

The period from 1200 GMT 10 April to 0000 GMT 11 April 1979, during which time several major tornadoes and severe thunderstorms, including the Wichita Falls tornado occurred was studied. A time adjusted, isentropic data set was used to analyze key parameters. Fourth order centered finite differences were used to compute the isallobaric, inertial advective, tendency, inertial advective geostrophic and ageostrophic winds. Explicit isentropic trajectories were computed through the isentropic, inviscid equations of motion using a 15 minute time step. Ageostrophic, geostrophic and total vertical motion fields were computed to judge the relative importance of ageostrophy in enhancing the vertical motion field. It is found that ageostrophy is symptomatic of those mass adjustments which take place during upper level jet streak propagation and can, in a favorable environment, act to increase and release potential instability over meso alpha time periods.

Moore, J. T.↗

NASA NTRS1992

Finite element Euler calculations of unsteady transonic cascade flows

A Galerkin finite element procedure incorporating an explicit Runge-Kutta time-stepping scheme has been developed in this work to solve unsteady transonic flow in cascades. The computational domain is discretized by a globally unstructured but locally structured blade-fitted deformable mesh. The Galerkin approximation is applied to the unsteady Euler equations based on a mixed Eulerian-Lagrangian description. The semi-discretized equations are integrated forward in time using a multistage Runge-Kutta scheme. An artificial dissipation operator of the type proposed by Jameson is adapted in the current scheme to capture shocks and suppress nonphysical oscillations. Phase-shifted boundary conditions are used to reduce the computational domain to a single reference passage. Results for both steady and unsteady transonic flows through cascades are presented and compared to existing finite volume solutions.

Hsiao, Chingteng↗

NASA NTRS1989

Recent advances in Runge-Kutta schemes for solving 3-D Navier-Stokes equations

A thin-layer Navier-Stokes has been developed for solving high Reynolds number, turbulent flows past aircraft components under transonic flow conditions. The computer code has been validated through data comparisons for flow past isolated wings, wing-body configurations, prolate spheroids and wings mounted inside wind-tunnels. The basic code employs an explicit Runge-Kutta time-stepping scheme to obtain steady state solution to the unsteady governing equations. Significant gain in the efficiency of the code has been obtained by implementing a multigrid acceleration technique to achieve steady-state solutions. The improved efficiency of the code has made it feasible to conduct grid-refinement and turbulence model studies in a reasonable amount of computer time. The non-equilibrium turbulence model of Johnson and King has been extended to three-dimensional flows and excellent agreement with pressure data has been obtained for transonic separated flow over a transport type of wing.

Vatsa, Veer N.↗

NASA NTRS1988

Explicit and implicit solution of the Navier-Stokes equations on a massively parallel computer

The design, implementation, and performance of a two-dimensional time-accurate Navier-Stokes solver for the CM2 supercomputer are described. The program uses a single processor for each grid point. Two different time-stepping methods have so far been implemented: an explicit third-order Runge-Kutta method and an implicit approximation-factorization method. The CM2 results are checked against those of a mature well-vectorized Cray 2 program, both for correctness and performance. The code is found to be correct, and the performance in some cases is up to several times that of the Cray 2.

Levit, Creon↗

NASA NTRS2016

Optimal Reorganization of NASA Earth Science Data for Enhanced Accessibility and Usability for the Hydrology Community

A long-standing "Digital Divide" in data representation exists between the preferred way of data access by the hydrology community and the common way of data archival by earth science data centers. Typically, in hydrology, earth surface features are expressed as discrete spatial objects (e.g., watersheds), and time-varying data are contained in associated time series. Data in earth science archives, although stored as discrete values (of satellite swath pixels or geographical grids), represent continuous spatial fields, one file per time step. This Divide has been an obstacle, specifically, between the Consortium of Universities for the Advancement of Hydrologic Science, Inc. and NASA earth science data systems. In essence, the way data are archived is conceptually orthogonal to the desired method of access. Our recent work has shown an optimal method of bridging the Divide, by enabling operational access to long-time series (e.g., 36 years of hourly data) of selected NASA datasets. These time series, which we have termed "data rods," are pre-generated or generated on-the-fly. This optimal solution was arrived at after extensive investigations of various approaches, including one based on "data curtains." The on-the-fly generation of data rods uses "data cubes," NASA Giovanni, and parallel processing. The optimal reorganization of NASA earth science data has significantly enhanced the access to and use of the data for the hydrology user community.

data rods↗

NASA NTRS1985

High-latitude filtering in a global grid-point model using model normal modes

A normal modes expansion technique is applied to perform high latitude filtering in the GLAS fourth order global shallow water model with orography. The maximum permissible time step in the solution code is controlled by the frequency of the fastest propagating mode, which can be a gravity wave. Numerical methods are defined for filtering the data to identify the number of gravity modes to be included in the computations in order to obtain the appropriate zonal wavenumbers. The performances of the model with and without the filter, and with a time tendency and a prognostic field filter are tested with simulations of the Northern Hemisphere winter. The normal modes expansion technique is shown to leave the Rossby modes intact and permit 3-5 day predictions, a range not possible with the other high-latitude filters.

Takacs, L. L.↗

NASA NTRS1993

Multigrid methods for numerical simulation of laminar diffusion flames

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

Liu, C.↗

NASA NTRS1976

Thermal instability in post-flare plasmas

The cooling of post-flare plasmas is discussed and the formation of loop prominences is explained as due to a thermal instability. A one-dimensional model was developed for active loop prominences. Only the motion and heat fluxes parallel to the existing magnetic fields are considered. The relevant size scales and time scales are such that single-fluid MHD equations are valid. The effects of gravity, the geometry of the field and conduction losses to the chromosphere are included. A computer code was constructed to solve the model equations. Basically, the system is treated as an initial value problem (with certain boundary conditions at the chromosphere-corona transition region), and a two-step time differencing scheme is used.

Antiochos, S. K.↗

NASA NTRS1990

Solving unstructured grid problems on massively parallel computers

A highly parallel graph mapping technique that enables one to efficiently solve unstructured grid problems on massively parallel computers is presented. Many implicit and explicit methods for solving discretized partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The cost of this communication can negate the high performance promised by massively parallel computing. To eliminate this bottleneck, the graph of the irregular problem is mapped into the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. It is shown that using the heuristic mapping algorithm significantly reduces the communication time compared to a naive assignment of processes to processors.

Hammond, Steven W.↗

NASA NTRS1986

Numerical experiments with a symmetric high-resolution shock-capturing scheme

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

Yee, H. C.↗