High Spectral Accuracy Research Articles

Computation of leading-edge contamination

The leading-edge contamination (LEC) problem of an infinite-swept wing is computed by solving the full two-dimensional Navier–Stokes equation using a very high spectral accuracy compact scheme. The initial condition is given by the steady attachment-line boundary layer forming over the leading-edge of an infinite swept wing or a yawed cylinder. The contamination is shown as due to either a convecting or a stationary vortex far outside the attachment-line boundary layer at the leading edge. This mechanism is proposed to account for the sub-critical instability onset observed for attachment-line boundary layer. (The criticality is for Reynolds number (based on momentum thickness) exceeding 100––an empirically suggested value based on earlier experiments.) The presented results show the problem to be essentially two-dimensional. Inflow and outflow of computational domain are chosen so that we consider cases of both sub- and super-critical instabilities. The receptivity mechanism of leading-edge contamination for both cases is investigated with respect to different parameters. Finally, we have also analyzed the computed solutions by proper orthogonal decomposition (POD) to highlight the low-dimensional nature and to provide a quantitative measure of leading-edge contamination events.

The SCIAMACHY calibration/monitoring concept and first results

The Scanning Imaging Absorption Spectro meter for Atmospheric Chartograph y (SCIAMACHY) is a contribution to the ENVISAT satellite, which has been launched successfully in March 2002. SCIAMACHY determines the amount and distributions of a large number of atmospheric constituents by measuring Earthshine radiance and solar irradiance spectra simultaneously from the UV to the NIR in various viewing geometries. The scientific goals of the SCIAMACHY mission can only be reached by an instrument having a high spectral and radiometric accuracy and stability. For example, to determine global NO 2 concentrations SCIAMACHY measurements need to be sensitive to differential spectral structures down to the order of 10 −4. These requirements can only be met by an appropriate instrument design in combination with both on-ground and in-flight calibration and monitoring. This paper gives an overview on the SCIAMACHY calibration and monitoring concept and activities which are essential to ensure the high quality of SCIAMACHY data products throughout the instrument lifetime. Furthermore, first in-flight monitoring results are presented.

Spectral correction of the measurement CCD array

We find that the distribution of the spectral correction error on a spectrally corrected CCD array is dependent on the choice of both the correction filter and the lens angle of view. The distribution of the spectral correction error on the spectrally corrected CCD array is analyzed. We present a method of calculating of the spectral coefficient of the monochromatic transmission factor of the filter for CCD array spectral correction. A filter calculated in this manner ensures that the corrected CCD array has a known constant and high spectral accuracy throughout the whole surface of the array.

Incompressible Navier–Stokes solutions by a triangular spectral/ p element projection method

The application of the fractional step projection method recently proposed by Guermond and Quartapelle to the numerical approximation of unsteady Navier–Stokes solutions by means of a spectral/ p element method is considered. In particular we illustrate the second-order pressure correction technique and evaluate its accuracy properties in some test cases. Stability with respect to the compatibility condition between the approximation spaces for velocity and pressure is also addressed. The high (spectral) accuracy in space and the second-order accuracy in time are verified by two simple test cases with analytical solution. A more interesting problem is solved showing the ability of the method to produce very accurate results also for problems in complex geometries.

Spectral Schemes on Triangular Elements

The Poisson problem with homogeneous Dirichlet boundary conditions is considered on a triangle. The transformation from square to triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be implemented. Numerical experiments demonstrate the expected high spectral accuracy for smooth solutions. Furthermore, it is shown that finite difference preconditioning can be successfully employed to construct an efficient iterative solver. Then the convection–diffusion equation is considered. Here finite difference preconditioning with central differences leads to instability. However, using the first-order upstream scheme, we obtain a stable method. Finally, a domain decomposition technique is applied to the patching of rectangular and triangular elements.

Spectral Schemes on Triangular Elements

AbstractFirst we consider the Poisson Problem with homogeneous Dirichlet boundary conditions on a triangle. The mapping between square and triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be applied. Numerical experiments demonstrate the expected high spectral accuracy. Further, it is shown that finite difference preconditioning can be successfully applied in order to construct an efficient iterative solver. Finally, a domain decomposition technique is applied to the patching of rectangular and triangular elements.

Spectral Collocation on Triangular Elements

We consider the Poisson problem on a segment of the unit disc and on triangles. On the segment we transform the Poisson problem by means of polar coordinates. In these new coordinates we have a problem in a rectangle which can easily be mapped onto the square. Here standard Chebyshev collocation techniques can be applied. Then the segment is mapped onto a triangle where the same spectral scheme may be used. By numerical tests we observed the expected high spectral accuracy. Due to the corner singularity a singular behaviour of the solution can be expected. Here we improved the accuracy by auxiliary mapping techniques. Further, it is shown that finite difference preconditioning can be successfully applied in order to construct an efficient iterative solver. Finally, a domain decomposition technique is applied to the patching of a rectangular and a triangular element.

Spectral viscosity for convection dominated flow

A stabilized treatment of convection dominated flow problems with a high order spectral viscosity method is presented. This method stabilizes the spectral scheme and remains the high spectral accuracy by introducing some viscosity only to the highest Fourier or Chebyshev modes. In the practical computation the method is employed to the Chebyshev pseudospectral (or collocation) discretization of some singular perturbation problems.

Augmented-plane-wave calculation and measurements ofKandLx-ray spectra for solid Ni

X-ray absorption and emission $K$ and $L$ spectra for solid Ni were calculated using the band structure and wave functions obtained from our augmented-plane-wave program. High spectral resolution and accuracy were achieved by a careful treatment of the Ni potential, band structure, wave functions, dipole matrix elements, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-space integrations and interpolations, and broadening due to core level widths; however, core-hole many-electron effects on the final-state wave functions were not included. Measurements of nickel $K$ and $L$ absorption-edge spectra were carried out using a two-crystal spectrometer, and the resulting spectra were corrected for instrumental window effects. The experimental and theoretical absorption spectra show excellent overall agreement with respect to positions and strengths of corresponding structures although, at threshold, the experimental $K$ edge is somewhat rounded and the experimental $L$ edge enhanced, relative to the corresponding theoretical spectra. For the case of the emission spectra, the calculated $L$ spectrum is considerably broader than would be indicated by most of the experimental x-ray valence-band results.