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Results for “explicit time stepping”

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.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Very Large Eddy Simulation Technique for Noise Prediction and Control in Turbomachinery and Propulsion

The summer fellowship research project focused on further developing an advanced computational technique based on Very Large Eddy Simulation (VLES) for analysis and control of major sources of noise in turbomachinery and propulsion systems, including jet noise and fan noise. Major part of the work during the 10-week tenure dealt with implementing a low-order, implicit A-stable time-stepping scheme in the existing explicit VLES code of Dr. Ray Hixon. The preliminary plan of the work also included application of a new time marching formulation to the problem of viscous gust-airfoil interaction. Other research items selected for implementation (possibly in the future) included investigating a set of new subgrid turbulent models for the code, and code application to a number of test cases, including a supersonic jet and swirling flow downstream of a rotor stage.

Golubev, Vladimir V.↗
NASA NTRS1984

Nonlinear evolution of the lower-hybrid drift instability

The results of simulations of the lower-hybrid drift instability in a neutral sheet configuration are described. The simulations use an implict formulation to relax the usual time step limitations and thus extend previous explicit calculations to weaker gradients, larger mass ratios, and long times compared with the linear growth time. The numerical results give the scaling of the saturation level, heating rates, resistivity, and cross-field diffusion and a demonstration by comparison with a fluid electron model that dissipation in the lower-hybrid drift instability is caused by electron kinetic effects.

Brackbill, J. U.↗
NASA NTRS1992

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Joslin, Ronald D.↗
DOE OSTI2025

A review of high order strong stability preserving two-derivative explicit, implicit, and IMEX methods

High order strong stability preserving time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stable simulation of hyperbolic PDEs in a wide variety of application areas including fluid dynamics, magnetohydrodynamics, semiconductor devices, electromagnetics, and astrophysics. Over the past decade multiderivative time-stepping have been increasingly used for the time-evolution hyperbolic PDEs, so that the strong stability properties of these methods have become important. In this work we review sufficient conditions for a two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and different conditions on the second derivative. In particular we present the strong stability preserving theory for explicit and implicit two-derivative Runge–Kutta schemes, including a special condition on the second derivative under which these implicit methods may be unconditionally strong stability preserving. This special condition is natural for the stiff component of wide range of plasma physics problems, and can be useful in the context of strong stability preserving implicit-explicit multi-derivative Runge–Kutta schemes, where the time-step restriction is then independent of the stiff term. Lastly, we present the strong stability preserving theory for implicit-explicit multi-derivative general linear methods, and some novel second and third order methods where the time-step restriction is independent of the stiff term.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

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.↗
NASA NTRS1996

Ideas for Future GPS Timing Improvements

Having recently met stringent criteria for full operational capability (FOC) certification, the Global Positioning System (GPS) now has higher customer expectations than ever before. In order to maintain customer satisfaction, and the meet the even high customer demands of the future, the GPS Master Control Station (MCS) must play a critical role in the process of carefully refining the performance and integrity of the GPS constellation, particularly in the area of timing. This paper will present an operational perspective on several ideas for improving timing in GPS. These ideas include the desire for improving MCS - US Naval Observatory (USNO) data connectivity, an improved GPS-Coordinated Universal Time (UTC) prediction algorithm, a more robust Kalman Filter, and more features in the GPS reference time algorithm (the GPS composite clock), including frequency step resolution, a more explicit use of the basic time scale equation, and dynamic clock weighting. Current MCS software meets the exceptional challenge of managing an extremely complex constellation of 24 navigation satellites. The GPS community will, however, always seek to improve upon this performance and integrity.

Hutsell, Steven T.↗
NASA NTRS1991

Computational study of three dimensional viscous flow through a turbine cascade using a multi-domain spectral technique

The three dimensional viscous flow through a planar turbine cascade is numerically simulated by direct solution of the incompressible Navier-Stokes equations. Flow dependence in the spanwise direction is represented by direct expansion in Chebyshev polynomials, while the discretization on planes parallel to the endwalls is accomplished using the spectral element method. Elemental mapping from the physical to the computational space uses an algebraic mapping technique. A fractional time stepping method that consists of an explicit nonlinear convective step, an implicit pressure correction step, and an implicit viscous step is used to advance the Navier-Stokes equations forward in time. Results computed at moderate Reynolds numbers show a three dimensional endwall flow separation, a midspan separation of the blade suction surface boundary layer, and other three-dimensional features such as the presence of a saddle point flow in the endwall region. In addition, the computed skin friction lines are shown to be orthogonal to the surface vorticity lines, demonstrating the accuracy achievable in the present method.

Renaud, Earl W.↗
NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗
NASA NTRS1987

Grid generation and inviscid flow computation about cranked-winged airplane geometries

An algebraic grid generation procedure that defines a patched multiple-block grid system suitable for fighter-type aircraft geometries with fuselage and engine inlet, canard or horizontal tail, cranked delta wing and vertical fin has been developed. The grid generation is based on transfinite interpolation and requires little computational power. A finite-volume Euler solver using explicit Runge-Kutta time-stepping has been adapted to this grid system and implemented on the VPS-32 vector processor with a high degree of vectorization. Grids are presented for an experimental aircraft with fuselage, canard, 70-20-cranked wing, and vertical fin. Computed inviscid compressible flow solutions are presented for Mach 2 at 3.79, 7 and 10 deg angles of attack. Conmparisons of the 3.79 deg computed solutions are made with available full-potential flow and Euler flow solutions on the same configuration but with another grid system. The occurrence of an unsteady solution in the 10 deg angle of attack case is discussed.

Eriksson, L.-E.↗
NASA NTRS1987

A finite volume Euler calculation of the aerodynamics of transonic airfoil-vortex interaction

Unsteady inviscid transonic airfoil-vortex interaction is numerically analyzed by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables is used to form the numerical dissipation terms to stabilize the scheme. A velocity decomposition technique is applied to alleviate the problem of vortex diffusion by the numerical dissipation terms and to treat the interaction of a Rankine vortex with an airfoil accurately. Results obtained are compared with available numerical data.

Damodaran, Murali↗
NASA NTRS1988

Finite volume computation of unsteady inviscid rotational transonic flows past airfoils in rigid body motion

Unsteady inviscid transonic flow over airfoils in arbitrary rigid body motion is analyzed numerically by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables are used to form the numerical dissipation terms to stabilize the scheme. Unsteady calculations are started from converged steady-state solutions as initial conditions. Nonreflective boundary conditions are imposed on the far-field boundaries. Results are presented and, where possible, validated against available numerical and experimental data for airfoils subjected to a step change in angle of attack, airfoils oscillating and plunging in transonic flow, and airfoils immersed in a time-varying free stream.

Damodaran, Murali↗
NASA NTRS1987

Flow solution on a dual-block grid around an airplane

The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.

Eriksson, Lars-Erik↗
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 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 NTRS1993

Three-dimensional unstructured grid Euler method applied to turbine blades

Flow through a turbine annular cascade is calculated using a three-dimensional Euler method based on unstructured tetrahedral meshes. The equations are integrated in time using an explicit Runge-Kutta time-stepping scheme. The inviscid flux terms are discretized using a cell-centered finite-volume formulation with upwind flux-difference splitting. The tetrahedral meshes around the turbine blade are generated using an advancing-front technique with forced geometric periodicity between the blades. Good agreement is obtained between the present calculation and the experiment for both surface pressure distribution and flow behavior in the passage between the blades, demonstrating the capability of the present methodology for turbomachinery flow applications.

Kwon, Oh J.↗
NASA NTRS1993

Hypersonic flow computations around re-entry vehicles

The development of an algorithm for the solution of the compressible Euler equations at high Mach numbers on unstructured tetrahedral meshes is described. The basic algorithm is constructed in the form of a central difference scheme plus an explicit added artificial viscosity based upon fourth order differences of the solution. The stability of the solution in the vicinity of strong gradients is preserved by the incorporation of an additional artificial viscosity based upon a second order difference. Higher order accuracy is regained by using the ideas of flux corrected transport to limit the amount of added viscosity. The solution is advanced to steady state by means of an explicit multi-stage time-stepping method. The computational efficiency of the complete process is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analyzed to demonstrate the numerical performance of the proposed approach.

Peraire, J.↗