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Hussaini, M. Y.

Publications and source records attributed to Hussaini, M. Y..

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Spectral methods for partial differential equations

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid-dynamical applications are emphasized.

Hussaini, M. Y.↗
NASA NTRS1984

Spectral methods for the Euler equations: Chebyshev methods and shock-fitting

The Chebyshev spectral collocation method for the Euler gas-dynamic equations is described. It is used with shock fitting to compute several two-dimensional, gas-dynamic flows. Examples include a shock-acoustic wave interaction, a shock/vortex interaction, and the classical blunt body problem. With shock fitting, the spectral method has a clear advantage over second order finite differences in that equivalent accuracy can be obtained with far fewer grid points.

Hussaini, M. Y.↗
NASA NTRS1984

Spectral methods for the Euler equations: Fourier methods and shock-capturing

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one dimensional, periodic astrophysical ""nozzle'' problem.

Hussaini, M. Y.↗
NASA NTRS1984

Applications of spectral methods to turbulent magnetofluids in space and fusion research

Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas.

Montgomery, D.↗
NASA NTRS1984

Spectral methods for solution of the boundary-layer equations

The basic principles of spectral methods are reviewed, and their application to the two-dimensional incompressible boundary-layer equations is discussed. It is shown that spectral collocation methods provide an accuracy sufficient for engineering applications on extremely coarse grids, and the machine time requirements are small. Although for a given stream-wise discretization, the fully spectral scheme requires more computational effort than the marching scheme, the higher accuracy of the former yields a large net gain in efficiency when considered at equivalent error levels.

Streett, C. L.↗
NASA NTRS1983

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
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 NTRS1983

Viscous, resistive magnetohydrodynamic stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗
NASA NTRS1983

Spectral methods for partial differential equations

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized.

Hussaini, M. Y.↗
NASA NTRS1983

Spectral methods for inviscid, compressible flows

Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.

Hussaini, M. Y.↗
NASA NTRS1983

Spectral methods for the Euler equations

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of both Fourier and Chebyshev spectral collocation methods are provided. Filtering strategies for both shock-fitting and shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem. Examples of shock-fitting approaches include a shock/acoustic wave interaction, shock/vortex interaction, and the classical blunt body problem. While the shock capturing spectral method does not yet show a clear advantage over second-order finite differences, equivalent accuracy can be obtained using shock fitting with far fewer grid points.

Hussaini, M. Y.↗
NASA NTRS1983

Psuedospectral calculation of shock turbulence interactions

A Chebyshev-Fourier discretization with shock fitting is used to solve the unsteady Euler equations. The method is applied to shock interactions with plane waves and with a simple model of homogeneous isotropic turbulence. The plane wave solutions are compared to linear theory.

Zang, T. A.↗
NASA NTRS1983

Spectral multigrid methods for elliptic equations 2

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Zang, T. A.↗
NASA NTRS1983

Spectral multigrid methods with applications to transonic potential flow

Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil.

Streett, C. L.↗
NASA NTRS1983

Numerical computations of turbulence amplification in shock wave interactions

Numerical computations are presented which illustrate and test various effects pertinent to the amplification and generation of turbulence in shock wave turbulent boundary layer interactions. Several fundamental physical mechanisms are identified. Idealizations of these processes are examined by nonlinear numerical calculations. The results enable some limits to be placed on the range of validity of existing linear theories.

Zang, T. A.↗
NASA NTRS1983

Viscous, resistive MHD stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗
NASA NTRS1983

Ion wind drag reduction

In order to study the effect of ion wind on viscous drag, the equations of electrogasdynamics are solved numerically assuming the flow is incompressible, the electric field is steady and that the fluid velocity is negligible compared to ion drift velocity. The results obtained to date in a continuing theoretical and experimental research program are presented.

Malik, M. R.↗