Spectral methods for the Euler equations
Abstract
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.
- Publication:
-
NASA STI/Recon Technical Report A
- Pub Date:
- July 1983
- Bibcode:
- 1983STIA...8339420H
- Keywords:
-
- Compressible Flow;
- Euler Equations Of Motion;
- Finite Difference Theory;
- Finite Element Method;
- Spectral Methods;
- Circular Cylinders;
- Collocation;
- Fourier Analysis;
- Shock Wave Interaction;
- Vortices;
- Fluid Mechanics and Heat Transfer