SEARCH · Search NASA

Results for “pseudospectral method”

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 37 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Effect of spatial resolution on apparent sensitivity to initial conditions of a decaying flow as it becomes turbulent

In order to check for spurious chaos and obtain superior solutions for decaying Navier-Stokes flows, an investigation is conducted of the effect of spatial resolution on numerical results. The fourth-order finite difference method results obtained with grids of 32-cubed and 64-cubed points, and those of a pseudospectral method for 128-cubed points, indicate that the sensitivity of initially neighboring solutions to small changes in initial conditions increases with improving spatial resolution.

Deissler, Robert G.↗

NASA NTRS1989

Effect of spatial resolution on apparent sensitivity to initial conditions of a decaying flow as it becomes turbulent

Grids with 32(exp 3), 64(exp 3), and 128(exp 3) points are used in numerical solutions for a decaying flow. The sensitivity of initially neighboring solutions to small changes in initial conditions increases as the spatial resolution improves. A fourth-order finite-difference method is used for the solutions with 32(exp 3) and 64(exp 3) grid points, and a pseudospectral method is used for 128(exp 3) grid points. The latter solutions appear to be rather well-resolved, in spite of the formation of steep velocity gradients in the flow.

Deissler, Robert G.↗

NASA NTRS1987

Error analysis for spectral approximation of the Korteweg-De Vries equation

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Maday, Y.↗

NASA NTRS1989

Analysis of the low gravity tolerance of Bridgman-Stockbarger crystal growth. I - Steady and impulse accelerations

The effects of steady and impulse-type residual accelerations on dopant distributions during directional solidification in 2D and 3D 'generic' models of the Bridgman-Stockbarger technique are investigated using numerical methods. The calculations are based on the thermophysical properties of molten germanium doped with a low concentration of gallium. A Chebyshev collocation pseudospectral method is used for the solution of the governing momentum-, mass-, species-, and heat-transfer equations. Only convection caused by temperature gradients is considered. It is found that lateral nonuniformity in composition is very sensitive to the orientation of the steady component of the residual gravity vector and to the particular operating conditions under consideration. It is also found that laterally or radially averaged composition profiles are alone insufficient to describe the extent of residual convection in a spacecraft environment. The effects of impulse-type disturbances can be severe and can extend for times on the order of 1000 sec after the termination of the impulse.

Alexander, J. Iwan D.↗

NASA NTRS1975

Recent progress in numerical techniques for flow simulation

Recent developments in the use of numerical methods for fluid flow simulation show an increasing tendency to use numerical operators that can, in various ways, be factored. Use of methods having this property often increases the accuracy and efficiency of computer codes. Tracing the factorization property provides a unity to the basic concepts involved in the development of cyclic reduction, predictor-corrector, splitting, fast Fourier transform, and pseudospectral methods.-

Lomax, H.↗

NASA NTRS1993

Numerical simulation of thermocapillary flow under zero and low gravity conditions

This paper discusses the numerical solution methods and results of steady and unsteady thermocapillary (surface-tension) and buoyancy driven flows in 2D cavities and liquid columns. The 2D cavity was assumed to be square with one free surface with a zero Capillary number (i.e., the free surface was constrained to be flat). A pseudospectral method was used to solve steady and unsteady surface tension-driven and mixed buoyancy-surface tension flows in a square cavity. For the liquid column a finite-difference scheme based on a Picard iteration was used to solve for the flow, temperature and free surface shape. The surface of the liquid column was allowed to deform and, as for the 2D cavity, the surface tension was assumed to depend on temperature.

Alexander, J. I. D.↗

NASA NTRS1986

On the boundary treatment in spectral methods for hyperbolic systems

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Canuto, C.↗

NASA NTRS1987

On the boundary treatment in spectral methods for hyperbolic systems

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Canuto, Claudio↗

NASA NTRS1978

Large eddy simulation of incompressible turbulent channel flow

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Moin, P.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock vortex interactions

The interaction of a planar shock wave with one or more vortexes is computed using a pseudospectral method and a finite difference method. The development of the spectral method is emphasized. In both methods the shock wave is fitted as a boundary of the computational domain. The results show good agreement between both computational methods. The spectral method is, however, restricted to smaller time steps and requires use of filtering techniques.

Salas, M. D.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock-vortex interactions

The interaction of a shock wave with a hot spot, a single vortex and a vortex street is studied within the framework of the two dimensional compressible Euler equations. The numerical results obtained by the pseudospectral method and the finite difference MacCormack method are compared. In both the methods the shock wave is fitted as a boundary of the computational domain.

Salas, M. E.↗

NASA NTRS1983

Pseudospectral solution of two-dimensional gas-dynamic problems

Chebyshev pseudospectral methods are used to compute two dimensional smooth compressible flows. Grid refinement tests show that spectral accuracy can be obtained. Filtering is not needed if resolution is sufficiently high and if boundary conditions are carefully prescribed.

Kopriva, D. A.↗

NASA NTRS1984

Modeling of unsteady small disturbance transonic flow using parametric differentiation, pseudospectral analysis and finite-differencing

A procedure for solving the nonlinear unsteady small disturbance transonic equation is formulated. This procedure is a synthesis of a pseudospectral method, parametric differentiation, and finite differencing. It is equally applicable to lifting and nonlifting airfoils. The procedure is particularly well suited to aeroelastic stability studies that may require a set of affine solutions.

Brown, M.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock-vortex interactions

Salas, M. D.↗

NASA NTRS1986

Statistical properties and correlation functions for drift waves

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Horton, W.↗

NASA NTRS1986

Direct numerical simulations of a temporally evolving mixing layer subject to forcing

The vortical evolution of mixing layers subject to various types of forcing is numerically simulated using pseudospectral methods. The effect of harmonic forcing and random noise in the initial conditions is examined with some results compared to experimental data. Spanwise forcing is found to enhance streamwise vorticity in a nonlinear process leading to a slow, secondary growth of the shear layer. The effect of forcing on a chemical reaction is favorably compared with experimental data at low Reynolds numbers. Combining harmonic and subharmonic forcing is shown to both augment and later destroy streamwise vorticity.

Claus, Russell W.↗

NASA NTRS1989

Direct numerical simulations of a temporally evolving mixing layer subject to forcing

Claus, R. W.↗

NASA NTRS1989

The secondary flow and its stability for natural convection in a tall vertical enclosure

The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air and the time-periodic flow of oil are investigated, and descriptions of these flows using both physical and spectral approaches are presented. The time dependence of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The three-dimensional linear stabiltiy of the multicellular air flow is parametrically studied. The domain of stable two-dimensional cellular motion is found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550.

Chait, Arnon↗