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At least 109 records · Page 6

Polynomial elimination theory and non-linear stability analysis for the Euler equations

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Kennon, S. R.↗

Viscel: A general purpose computer program for analysis of linear viscoelastic structures, volume 2

The VISCEL program is a general purpose computer program developed for equilibrium analysis of linear viscoelastic structures. The program is written in FORTRAN 5 language to operate on the Univac 1108 computer under the EXEC 8 operating system. The program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form written for the IBM 7094 computer. Finite element matrix displacement approach coupled with the synchronized material property concept, utilizing incremental time steps, was adopted for the solution presented. The step-by-step procedure involves solution of recursive equations in the time domain, which takes into account the memory of material properties. Incremental and accumulative displacements and stresses are obtained at the end of each time step. In order to minimize the extent of computations resulting from accumulative effects of material memory, the program provides an option which enables the employment of constant time steps in the logarithmic scale. Program documentation is presented.

Gupta, K. K.↗

On the Numerical Convergence to Steady State of Hypersonic Flows Over Bodies with Concavities

Two recent numerical studies of hypersonic flows over bodies with concavities revealed problems with convergence to a steady state with an oft-used application of local-time-stepping. Both simulated flows showed a time-like, periodic shedding of vortices in a subsonic domain bounded by supersonic external flow although the simulations, using local-time-stepping, were not time accurate. Simple modifications to the numerical algorithm were implemented to enable implicit, first-order accurate in time simulations. Subsequent time-accurate simulations of the two test problems converged to a steady state. The baseline algorithm and modifications for temporal accuracy are described. The requirement for sub-iterations to achieve convergence is demonstrated. Failure to achieve convergence without time accuracy is conjectured to arise from temporal errors being continuously refocused into a subsonic domain.

Gnoffo, Peter A.↗

Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings

In engineering and aerospace applications, it is vital to operational success to have insight into the expected performance and health of physical systems. The field of prognostics and health management provides quantitative methods for monitoring, predicting, and managing system health. Prognostics algorithms can be employed to assess the current state of a system, propagate the system throughout time, and predict potential anomalies or failures that may occur. While they can provide accurate prediction results, effective prognostics algorithms can be challenging to use in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for future remaining useful life predictions. In this work, we implement new algorithmic approaches for prediction, quantitatively compare them via a battery degradation use-case, and provide recommendations of potential improvements to a prognostics framework. One approach to prediction is through sampling, whereby the current state of a physical system is sampled many times and each sample is propagated forward until failure is reached, resulting in a distribution of failure values. To improve the efficiency of this process, we implemented five new algorithmic approaches to prediction, including three distinct sampling methods (standard Monte Carlo, Quasi-Monte Carlo, and Latin Hypercube Sampling), a variable time step algorithm, and a variable sample size algorithm. To compare the algorithms, we employ a variety of metrics designed specifically to analyze both computational efficiency and model accuracy. Our metrics include accuracy to compare the average predicted value to ground truth, mean absolute deviation to illustrate dispersion, specific percentile error to describe accuracy within a user-defined risk tolerance, and code run-time. To quantitatively analyze our results, we employ a use-case of degradation of a Lithium-ion battery. We use an electrochemistry-based model to describe the current health state of the battery, and implement our prediction algorithms to propagate forward in time until end-of-discharge (EOD) is reached. Notably, through this work it was found that none of our sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. We find that while the sampling methods are unique, the distributions they generate are similar, ultimately producing final predictions that are nearly identical. In exploring the effect of the time step within the prediction algorithm, we found that prediction accuracy was highly dependent on the time step used, and that implementing a variable time step within a particular prediction may provide an increase in computational efficiency while also maintaining prediction accuracy. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment can result in improved computation speed and maintained prediction accuracy. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency.

prognostics↗

Rain volume estimation over areas using satellite and radar data

The feasibility of rain volume estimation over fixed and floating areas was investigated using rapid scan satellite data following a technique recently developed with radar data, called the Area Time Integral (ATI) technique. The radar and rapid scan GOES satellite data were collected during the Cooperative Convective Precipitation Experiment (CCOPE) and North Dakota Cloud Modification Project (NDCMP). Six multicell clusters and cells were analyzed to the present time. A two-cycle oscillation emphasizing the multicell character of the clusters is demonstrated. Three clusters were selected on each day, 12 June and 2 July. The 12 June clusters occurred during the daytime, while the 2 July clusters during the nighttime. A total of 86 time steps of radar and 79 time steps of satellite images were analyzed. There were approximately 12-min time intervals between radar scans on the average.

Doneaud, A. A.↗

Least-squares finite element methods for compressible Euler equations

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Jiang, Bo-Nan↗

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗

Explicit numerical formulas of improved stability and accuracy for the solution of parabolic equations

A class of explicit numerical formulas which involve next nearest neighbor as well as nearest neighbor points are explored in this paper. These formulas are formal approximations to the linear parabolic partial-differential equation of first order in time and second order in distance. It was found that some of these formulas can employ time steps as much as four times that for the conventional explicit technique without becoming unstable. Others showed improved accuracy for a given time step and spatial grid spacing. One formula achieved a steady-state solution of specified accuracy for an example problem in less than 4 percent of the total computational time required by the conventional explicit technique.

Olstad, W. B.↗

Time Relevance of Convective Weather Forecast for Air Traffic Automation

The Federal Aviation Administration (FAA) is handling nearly 120,000 flights a day through its Air Traffic Management (ATM) system and air traffic congestion is expected to increse substantially over the next 20 years. Weather-induced impacts to throughput and efficiency are the leading cause of flight delays accounting for 70% of all delays with convective weather accounting for 60% of all weather related delays. To support the Next Generation Air Traffic System goal of operating at 3X current capacity in the NAS, ATC decision support tools are being developed to create advisories to assist controllers in all weather constraints. Initial development of these decision support tools did not integrate information regarding weather constraints such as thunderstorms and relied on an additional system to provide that information. Future Decision Support Tools should move towards an integrated system where weather constraints are factored into the advisory of a Decision Support Tool (DST). Several groups such at NASA-Ames, Lincoln Laboratories, and MITRE are integrating convective weather data with DSTs. A survey of current convective weather forecast and observation data show they span a wide range of temporal and spatial resolutions. Short range convective observations can be obtained every 5 mins with longer range forecasts out to several days updated every 6 hrs. Today, the short range forecasts of less than 2 hours have a temporal resolution of 5 mins. Beyond 2 hours, forecasts have much lower temporal. resolution of typically 1 hour. Spatial resolutions vary from 1km for short range to 40km for longer range forecasts. Improving the accuracy of long range convective forecasts is a major challenge. A report published by the National Research Council states improvements for convective forecasts for the 2 to 6 hour time frame will only be achieved for a limited set of convective phenomena in the next 5 to 10 years. Improved longer range forecasts will be probabilistic as opposed to the deterministic shorter range forecasts. Despite the known low level of confidence with respect to long range convective forecasts, these data are still useful to a DST routing algorithm. It is better to develop an aircraft route using the best information available than no information. The temporally coarse long range forecast data needs to be interpolated to be useful to a DST. A DST uses aircraft trajectory predictions that need to be evaluated for impacts by convective storms. Each time-step of a trajectory prediction n&s to be checked against weather data. For the case of coarse temporal data, there needs to be a method fill in weather data where there is none. Simply using the coarse weather data without any interpolation can result in DST routes that are impacted by regions of strong convection. Increasing the temporal resolution of these data can be achieved but result in a large dataset that may prove to be an operational challenge in transmission and loading by a DST. Currently, it takes about 7mins retrieve a 7mb RUC2 forecast file from NOAA at NASA-Ames Research Center. A prototype NCWF6 1 hour forecast is about 3mb in size. A Six hour NCWFG forecast with a 1hr forecast time-step will be about l8mb (6 x 3mb). A 6 hour NCWF6 forecast with a l5min forecast time-step will be about 7mb (24 x 3mb). Based on the time it takes to retrieve a 7mb RUC2 forecast, it will take approximately 70mins to retrieve a 6 hour NCWF forecast with 15min time steps. Until those issues are addressed, there is a need to develop an algorithm that interpolates between these temporally coarse long range forecasts. This paper describes a method of how to use low temporal resolution probabilistic weather forecasts in a DST. The beginning of this paper is a description of some convective weather forecast and observation products followed by an example of how weather data are used by a DST. The subsequent sections will describe probabilistic forecasts followed by a descrtion of a method to use low temporal resolution probabilistic weather forecasts by providing a relevance value to these data outside of their valid times.

Chan, William N.↗

Between a Map and a Data Rod

A Digital Divide has long stood between how NASA and other satellite-derived data are typically archived (time-step arrays or maps) and how hydrology and other point-time series oriented communities prefer to access those data. In essence, the desired method of data access is orthogonal to the way the data are archived. Our approach to bridging the Divide is part of a larger NASA-supported data rods project to enhance access to and use of NASA and other data by the Consortium of Universities for the Advancement of Hydrologic Science, Inc. (CUAHSI) Hydrologic Information System (HIS) and the larger hydrology community. Our main objective was to determine a way to reorganize data that is optimal for these communities. Two related objectives were to optimally reorganize data in a way that (1) is operational and fits in and leverages the existing Goddard Earth Sciences Data and Information Services Center (GES DISC) operational environment and (2) addresses the scaling up of data sets available as time series from those archived at the GES DISC to potentially include those from other Earth Observing System Data and Information System (EOSDIS) data archives. Through several prototype efforts and lessons learned, we arrived at a non-database solution that satisfied our objectivesconstraints. We describe, in this presentation, how we implemented the operational production of pre-generated data rods and, considering the tradeoffs between length of time series (or number of time steps), resources needed, and performance, how we implemented the operational production of on-the-fly (virtual) data rods. For the virtual data rods, we leveraged a number of existing resources, including the NASA Giovanni Cache and NetCDF Operators (NCO) and used data cubes processed in parallel. Our current benchmark performance for virtual generation of data rods is about a years worth of time series for hourly data (9,000 time steps) in 90 seconds. Our approach is a specific implementation of the general optimal strategy of reorganizing data to match the desired means of access. Results from our project have already significantly extended NASA data to the large and important hydrology user community that has been, heretofore, mostly unable to easily access and use NASA data.

machine learning↗

Numerical solution methods for viscoelastic orthotropic materials

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Gramoll, K. C.↗

A time-accurate multiple-grid algorithm

A time-accurate multiple-grid algorithm is described. The algorithm allows one to take much larger time steps with an explicit time-marching scheme than would otherwise be the case. Sample calculations of a scalar advection equation and the Euler equations for an oscillating airfoil are shown. For the oscillating airfoil, time steps an order of magnitude larger than the single-grid algorithm are possible.

Jespersen, D. C.↗

A cell-vertex multigrid method for the Navier-Stokes equations

A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.

Radespiel, R.↗

An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Radespiel, R.↗

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

Atkins, Harold↗

A multi-block multigrid method for the solution of the Euler and Navier-Stokes equations for three-dimensional flows

A multi-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell-vertex method which employs central-difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques, and variable-coefficient numerical smoothing results in an efficient and robust scheme. The multi-block strategy places the block loop within the Runge-Kutta loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one- and two-block calculations in which the two-block grid is generated by splitting the one-block grid. Results are presented for both Euler and Navier-Stokes computations of wings and wing-fuselage combinations.

Atkins, H. L.↗

Enhancing Scalability for FUN3D Rotorcraft Simulations with Yoga: an Overset Grid Assembler

FUN3D, an unstructured grid Navier-Stokes CFD code is capable of overset grid simu- lations, but does not have an internal method for assembling an overset grid system from a group of component grids. FUN3D currently relies on the third party codes Suggar++ and DiRTlib to perform domain assembly and provide intergrid connectivity for overset simulations. Rotorcraft simulations with moving, deforming blades require domain assembly and mesh deformation at each time step. For these simulations, the three primary drivers of computational cost for each time step are: deforming the mesh, performing domain assembly, and performing subiterations of the flow solver. FUN3D exhibits strong and weak scalability for the flow solver subiterations and the mesh deformation. However, FUN3D is currently hardwired directly to the serial version of Suggar++, which has a fixed cost for a given mesh system. Therefore, domain assembly begins to dominate the total cost of each time step as grid systems become larger. An integrated method for parallel domain assembly is presented that addresses scalability for large grid systems. Restructuring within FUN3D to accommodate integrated domain assembly is also discussed, which could enable use of the parallel Suggar++ library.

Cameron T Druyor↗

Time-accurate Navier-Stokes calculations with multigrid acceleration

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.

Melson, N. Duane↗