Engineering topics

Turkel, E.

Publications and source records attributed to Turkel, E..

At least 73 records · Page 4

NASA NTRS1983

Progress in computational physics

Recent progress in computational methods for time dependent fluid dynamics is presented. The emphasis is on advances applicable to large scale systems with the connection between the numerics and the physics of the code stressed. All aspects of a working code are discussed including such topics as initialization, boundary conditions, grid generation in addition to algorithmic advances. One sometimes uses a time dependent method as an iteration procedure to reach a steady state solution. Work in accelerating the convergence to the steady state is also surveyed.

Turkel, E.↗

NASA NTRS1982

Far field boundary conditions for compressible flows

Previously announced in STAR as N81-33857

Bayliss, A.↗

NASA NTRS1982

Simulation of the fluctuating field of a forced jet

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected and the effect of nonlinearity is studied. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales.

Bayliss, A.↗

NASA NTRS1982

Simulation of the fluctuating field of a forced jet

Bayliss, A.↗

NASA NTRS1981

Far field conditions for compressible flows

The numerical treatment of exterior regions requires a method to convert the problem to one in a bounded region. One method is to truncate the unbounded region at some finite, artificial surface. This creates a finite computational region at the expense of imposing boundary conditions at the artificial boundary. If the problem has wave-like solutions near infinity, then these boundary conditions must simulate the radiation of energy out of the computational domain and towards infinity. Incorrect specification of these radiation boundary conditions can cause spurious reflected waves to be generated at the artificial boundary. Radiation boundary conditions which have the following properties were constructed: to accurately simulate the radiation of energy out of the computational domain; to accomplish the simulation with an accuracy which improves as fast as feasible as the artificial surface is moved outward; and to accelerate convergence to the steady state (by minimizing spurious reflections).

Bayliss, A.↗

NASA NTRS1981

Stability of pseudospectral and finite-difference methods for variable coefficient problems

It is shown that pseudospectral approximation to a special class of variable coefficient one-dimensional wave equations is stable and convergent even though the wave speed changes sign within the domain. Computer experiments indicate similar results are valid for more general problems. Similarly, computer results indicate that the leapfrog finite-difference scheme is stable even though the wave speed changes sign within the domain. However, both schemes can be asymptotically unstable in time when a fixed spatial mesh is used.

Gottlieb, D.↗

NASA NTRS1981

On the interaction of a sound pulse with the shear layer of an axisymmetric jet

The behavior of a sound pulse from a simulated source in a jet is investigated both experimentally and numerically. Both approaches show that in the low and medium frequencies the far field acoustic power exhibits and marked amplification as the flow velocity increases. Experimentally this changes to an attenuation at the higher frequencies which cannot be computed by the numerical model. This amplification is traced to shear noise terms which trigger the instability waves that are inherent within the flow.

Maestrello, L.↗

NASA NTRS1980

Radiation boundary conditions for wave-like equations

In the numerical computation of hyperbolic equations it is not practical to use infinite domains; instead, the domain is truncated with an artificial boundary. In the present study, a sequence of radiating boundary conditions is constructed for wave-like equations. It is proved that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r exp -m-1/2) for the m-th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature of the boundary conditions.

Bayliss, A.↗

NASA NTRS1980

On time discretizations for spectral methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Gottlieb, D.↗

NASA NTRS1980

On the practical use of high-order methods for hyperbolic systems

The paper tests a number of high order methods on a variety of dynamic problems in one, two, and three space dimensions. The problems covered include wave propagation phenomena as well as an asymptotic approach to a steady state. Consideration is given to both smooth and shocked flows. It is shown that the methods compared require only minor modifications of many existing second-order schemes. Further, the results show that significant gains can be expected from the use of fourth-order methods. Finally, spectral methods are also considered for some of the problems presented.

Turkel, E.↗

NASA NTRS1980

Boundary conditions for the numerical solution of elliptic equations in exterior regions

Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used.

Bayliss, A.↗

NASA NTRS1980

Numerical methods for large-scale time-dependent partial differential equations

The factors that influence the choice of a numerical solution scheme for large-scale time-dependent partial differential equations are examined with emphasis on the treatment of boundaries. Consideration is given to standard boundary treatments, moving boundaries, and artificial boundaries simulating an infinite domain. Implicit methods and applications to specific problems are discussed with special attention to shocks and steady state solutions.

Turkel, E.↗

NASA NTRS1979

Experimental and numerical results on a shear layer excited by a sound pulse

The behavior of a sound in a jet was investigated. It is verified that the far-field acoustic power increased with flow velocity for the lower and medium frequency range. Experimentally, an attenuation at higher frequencies is also observed. This increase is found numerically to be due primarily to the interactions between the mean vorticity and the fluctuation velocities. Spectral decomposition of the real time data indicates that the power increase occurs in the low and middle frequency range, where the local instability waves have the largest spatial growth rate. The connection between this amplification and the local instability waves is discussed.

Maestrello, L.↗

NASA NTRS1979

Numerical methods for large-scale, time-dependent partial differential equations

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Turkel, E.↗

NASA NTRS1979

Dynamic acoustics for the STAR-100

An algorithm is described to compute time dependent acoustic waves in a jet. The method differs from previous methods in that no harmonic time dependence is assumed, thus permitting the study of nonharmonic acoustical behavior. Large grids are required to resolve the acoustic waves. Since the problem is nonstiff, explicit high order schemes can be used. These have been adapted to the STAR-100 with great efficiencies and permitted the efficient solution of problems which would not be feasible on a scalar machine.

Bayliss, A.↗

NASA NTRS1979

Explicit large time-step schemes for the shallow water equations

Modifications to explicit finite difference schemes for solving the shallow water equations for meteorological applications by increasing the time step for the fast gravity waves are analyzed. Terms associated with the gravity waves in the shallow water equations are treated on a coarser grid than those associated with the slow Rossby waves, which contain much more of the available energy and must be treated with higher accuracy, enabling a several-fold increase in time step without degrading the accuracy of the solution. The method is presented in Cartesian and spherical coordinates for a rotating earth, using generalized leapfrog, frozen coefficient, and Fourier filtering finite difference schemes. Computational results verify the numerical stability of the approach.

Turkel, E.↗

NASA NTRS1979

Boundary conditions for exterior acoustic problems

Problems of acoustics are generally posed in unbounded regions. Numerical computations require that the infinite regions be truncated with artificial finite boundaries. Boundary conditions must be developed at these artificial boundaries which approximate the conditions for outgoing waves. These conditions should be asymptotic in the distance of the boundaries from the source terms and should give rise to well posed problems interior to fairly arbitrary regions, which can be chosen on the basis of computational efficiency rather than for mathematical (i.e., well posedness) reasons. A family of such conditions is presented and their properties are discussed. These conditions can be thought of as extensions of the Sommerfeld radiation condition for outgoing waves.

Bayliss, A.↗

NASA NTRS1978

Computation of acoustic waves in a jet

A numerical treatment of acoustic waves in a jet is described. The full time dependent Euler equations are used in both linear and nonlinear formulations. The computational region of integration is artificially bounded and boundary conditions are developed to simulate outgoing waves and to enable the computational domain to be substantially restricted. Higher order methods and coordinate transformations are introduced to further reduce the number of grid points as well as to increase the efficiency of the program. Numerical results are presented for time harmonic sources as well as for sources with more complicated time dependence.

Bayliss, A.↗