SEARCH · Engineering Papers

Results for “time step”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS2000

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗

NASA NTRS1988

An implicit Navier-Stokes analysis of turbine rotor-stator interaction

An implicit Navier-Stokes analysis using a single deforming mesh has been developed for the unsteady rotor-stator interaction problem. The technique has been used to simulate the flow through a turbine stator-rotor stage. Periodic two-dimensional solutions have been obtained using 1000 time steps per cycle without iteration at each time step. Computed surface pressure distributions compare favorably with experimental data available for this configuration.

Gibeling, Howard J.↗

NASA NTRS2003

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

Lin, Shian-Jiann↗

NASA NTRS2004

Agglomeration Multigrid for an Unstructured-Grid Flow Solver

An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.

Frink, Neal↗

NASA NTRS1992

A comparison of artificial compressibility and fractional step methods for incompressible flow computations

We have applied and compared the efficiency and accuracy of two commonly used numerical methods for the solution of Navier-Stokes equations. The artificial compressibility method augments the continuity equation with a transient pressure term and allows one to solve the modified equations as a coupled system. Due to its implicit nature, one can have the luxury of taking a large temporal integration step at the expense of higher memory requirement and larger operation counts per step. Meanwhile, the fractional step method splits the Navier-Stokes equations into a sequence of differential operators and integrates them in multiple steps. The memory requirement and operation count per time step are low, however, the restriction on the size of time marching step is more severe. To explore the strengths and weaknesses of these two methods, we used them for the computation of a two-dimensional driven cavity flow with Reynolds number of 100 and 1000, respectively. Three grid sizes, 41 x 41, 81 x 81, and 161 x 161 were used. The computations were considered after the L2-norm of the change of the dependent variables in two consecutive time steps has fallen below 10(exp -5).

Chan, Daniel C.↗

NASA NTRS2013

Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities

The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.

Yee, Helen M. C.↗

NASA NTRS1979

Shuttle program. Onorbit navigation integrator results for typical shuttle orbits

Three types of navigation onorbit numerical integrators were evaluated: (1) power integrators with no delta-V incorporation, just coasting (using Taylor series expansion integrators); (2) coasting integrators using the Cowell method of special perturbations; and (3) coasting integrator using the Pines variation of parameter perturbation method. Results show that the super G integrator is a very simple and effective for 2 and 4 second time steps. Since IMU delta-V data can be easily incorporated in the integration scheme, its use as the standard onorbit navigation propagator for the maintenance of the current state was implemented in the onboard navigation software. The Pines formulation method with a Runge-Kutta-Gill fourth-order integrator method produces excellent results up to 300 second time steps. On orbit prediction with this method was implemented in the onboard onorbit navigation scheme. The Runge-Kutta third order, using Cowell's method, is an excellent general purpose determination integrator for time steps up to a 60 second duration.

Olszewski, O. W.↗

NASA NTRS2011

Tracking Object Existence From an Autonomous Patrol Vehicle

An autonomous vehicle patrols a large region, during which an algorithm receives measurements of detected potential objects within its sensor range. The goal of the algorithm is to track all objects in the region over time. This problem differs from traditional multi-target tracking scenarios because the region of interest is much larger than the sensor range and relies on the movement of the sensor through this region for coverage. The goal is to know whether anything has changed between visits to the same location. In particular, two kinds of alert conditions must be detected: (1) a previously detected object has disappeared and (2) a new object has appeared in a location already checked. For the time an object is within sensor range, the object can be assumed to remain stationary, changing position only between visits. The problem is difficult because the upstream object detection processing is likely to make many errors, resulting in heavy clutter (false positives) and missed detections (false negatives), and because only noisy, bearings-only measurements are available. This work has three main goals: (1) Associate incoming measurements with known objects or mark them as new objects or false positives, as appropriate. For this, a multiple hypothesis tracker was adapted to this scenario. (2) Localize the objects using multiple bearings-only measurements to provide estimates of global position (e.g., latitude and longitude). A nonlinear Kalman filter extension provides these 2D position estimates using the 1D measurements. (3) Calculate the probability that a suspected object truly exists (in the estimated position), and determine whether alert conditions have been triggered (for new objects or disappeared objects). The concept of a probability of existence was created, and a new Bayesian method for updating this probability at each time step was developed. A probabilistic multiple hypothesis approach is chosen because of its superiority in handling the uncertainty arising from errors in sensors and upstream processes. However, traditional target tracking methods typically assume a stationary detection volume of interest, whereas in this case, one must make adjustments for being able to see only a small portion of the region of interest and understand when an alert situation has occurred. To track object existence inside and outside the vehicle's sensor range, a probability of existence was defined for each hypothesized object, and this value was updated at every time step in a Bayesian manner based on expected characteristics of the sensor and object and whether that object has been detected in the most recent time step. Then, this value feeds into a sequential probability ratio test (SPRT) to determine the status of the object (suspected, confirmed, or deleted). Alerts are sent upon selected status transitions. Additionally, in order to track objects that move in and out of sensor range and update the probability of existence appropriately a variable probability detection has been defined and the hypothesis probability equations have been re-derived to accommodate this change. Unsupervised object tracking is a pervasive issue in automated perception systems. This work could apply to any mobile platform (ground vehicle, sea vessel, air vehicle, or orbiter) that intermittently revisits regions of interest and needs to determine whether anything interesting has changed.

Wolf, Michael↗

NASA NTRS1987

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1989

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

Keeling, Stephen L.↗

NASA NTRS1990

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗

NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Yee, H. C.↗

NASA NTRS2002

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

Sjoegreen, Bjoern↗

NASA NTRS1988

Spatio-temporal adaptation algorithm for two-dimensional reacting flows

A spatio-temporal adaptive algorithm for solving the unsteady Euler equations with chemical source terms is presented. Quadrilateral cells are used in two spatial dimensions which allow for embedded meshes tracking moving flow features with spatially varying time-steps which are multiples of global minimum time-steps. Blast wave interactions corresponding to a perfect gas (frozen) and a Lighthill dissociating gas (nonequilibrium) are considered for circular arc cascade and 90 degree bend duct geometries.

Pervaiz, Mehtab M.↗

NASA NTRS1992

The relationship between pressure-based and density-based algorithms

The PISO, pressure-based algorithm, is compared with implicit time-marching systems to ascertain their similarities and differences. Both methods are expressed in vector form for comparison purposes. The vector form of the PISO method is triangular, allowing an uncoupled solution procedure, while the Euler implicit method requires the simultaneous solution of all equations. Upwind differencing is performed according to the direction of the eigenvalues in both systems, but this is the particle velocity in the PISO method and the acoustic velocity in the Euler method. Vector stability calculations show that the PISO method is conditionally stable depending on the time step, but that it provides adequate damping at small time steps to enable good convergence. Unconditional stability can be provided by retaining the energy coupling terms in the time derivative. Transforming the Euler implicit equations to the PISO variables along with a modification of the time derivatives gives the density-based method the same amplification factors at low speeds as the pressure-based method without affecting their behavior at high speeds.

Merkle, Charles L.↗

NASA NTRS2009

Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-time-stepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard second-order, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

Vatsa, Veer N.↗

NASA NTRS1998

LAPS Lidar Measurements at the ARM Alaska Northslope Site (Support to FIRE Project)

This report consists of data summaries of the results obtained during the May 1998 measurement period at Barrow Alaska. This report does not contain any data interpretation or analysis of the results which will follow this activity. This report is forwarded with a data set on magnetic media which contains the reduced data from the LAPS lidar in 15 minute intervals. The data was obtained during the period 15-30 May 1998. The measurement period overlapped with several aircraft flights conducted by NASA as part of the FIRE project. The report contains a summary list of the data obtained plus figures that have been prepared to help visualize the measurement periods. The order of the presentation is as follows: Section 1. A copy of the Statement of Work for the planned activity of the second measurement period at the ARM Northslope site is provided. Section 2. A list of the data collection periods shows the number of one minute data records stored during each hour of operation and the corresponding size (Mbytes) of the one hour data folders. The folder and file names are composed from the year, month, day, hour and minute. The date/time information is given in UTC for easier comparison with other data sets. Section 3. A set of 4 comparisons between the LAPS lidar results and the sondes released by the ARM scientists from a location nearby the lidar. The lidar results show the +/- 1 sigma statistical error on each of the independent 75 m altitude bins of the data. This set of 4 comparisons was used to set and validate the calibration value which was then used for the complete data set. Section 4. A set of false color figures with up to 10 hours of specific humidity measurements are shown in each graph. Two days of measurements are shown on each page. These plots are crude representations of the data and permit a survey which indicates when the clouds were very low or where interesting events may occur in the results. These plots are prepared using the real time sequence plot program which has no smoothing in either the altitude or time (except that you are allowed to pick the integration time and time step. All of these plots were prepared with 15 minute integration and 5 minute time step. Section 5. A set of time sequence data for all of the extended observation periods are shown with a smoothing algorithm from the Matlab plotting library. Most of these data are integrated for 5 minutes and stepped at I minute intervals but several plots are shown with both 15 minute integration and 5 minute steps. The upper level on these data was selected and converted to the white background where the error in the specific humidity reached 25%. Section 6. The set of one hour integrated plots shown with up to 4 hours per page are provided- from the real time analysis snapshot program. The only difference in these plots and the real time display is that the plots are stopped at an altitude where the error appears to be too large for the data to contain any meaningful information.

Philbrick, C. Russell↗

NASA NTRS2003

Choice of Variables and Preconditioning for Time Dependent Problems

We consider the use of low speed preconditioning for time dependent problems. These are solved using a dual time step approach. We consider the effect of this dual time step on the parameter of the low speed preconditioning. In addition, we compare the use of two sets of variables, conservation and primitive variables, to solve the system. We show the effect of these choices on both the convergence to a steady state and the accuracy of the numerical solutions for low Mach number steady state and time dependent flows.

Turkel, Eli↗