Abstract
Numerical experiments are performed to compare the accuracy obtained when physical and transform space filters are used to smooth the oscillations in Fourier collocation approximations to discontinuous solutions of a linear wave equation. High-order accuracy can be obtained away from a discontinuity but the order is strongly filter dependent. Polynomial order accuracy is demonstrated when smooth high-order Fourier filters are used. Spectral accuracy is obtained with the physical space filter of Gottlieb and Tadmor.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cornille, P. (1982). A pseudospectral scheme for the numerical calculation of shocks,J. Comp. Phys. 47, 146–159.
Gottlieb, D., Hussaini, M. Y., and Orszag, S. A. (1984). Theory and applications of spectral methods, inSpectral Methods for Partial Differential Equations, Voigt, R. G., Gottlieb, D., Hussaini, M. Y. (eds.), SIAM (Philadelphia), pp. 1–54.
Gottlieb, D., Lustman, L., and Orszag, S. A. (1981). Spectral calculations of one-dimensional inviscid compressible flows,SIAM J. Sci. Statis. Comput. 2, 296–310.
Gottlieb, D., and Tadmor, E. (1985). Recovering Pointwise Values of Discontinuous Data Within Spectral Accuracy, ICASE Rept. No. 85-3.
Hamming, R. W. (1983).Digital Filters (2nd Ed.), Prentice-Hall, Englewood Cliffs.
Hussaini, M. Y., Kopriva, D. A., Salas, M. D., and Zang, T. A. (1985). Spectral methods for the Euler equations: Part I-Fourier methods and shock capturing,AI A A J. 23, 64–70.
Kopriva, D. A., Zang, T. A., Salas, M. D., and Hussaini, M. Y. (1984). Pseudospectral solution of two-dimensional gas-dynamics problems, inProc. 5th GAMM Conference on Numerical Methods in Fluid Mechanics, Pandolfi, M., and Piva, R. (eds.), Vieweg & Sohn, Braunschweig, Wiesbaden, pp. 185–192.
Majda, A., McDonough, J., and Osher, S. (1978). The Fourier method for nonsmooth initial data,Math. Comp. 32, 1041–1081.
Sakell, L. (1984). Pseudospectral solutions of one- and two-dimensional inviscid flows with shock waves,AIAA J. 22, 929–934.
Tadmor, E. (1984). The Exponential Accuracy of Fourier and Tchebyshev Differencing Methods, ICASE Rept No. 84-40.
Taylor, T. D., Myers, R. B., and Albert, J. H. (1981). Pseudospectral calculations of shock waves, rarefaction waves and contact surfaces,Comput. and Fluids 9, 469–473.
Van Albada, G. D., Van Leer, B., and Roberts, W. W. Jr. (1982). A comparative study of computational methods in cosmic gas dynamics,Astron. and Astrophys. 108, 76–84.
Zang, T. A., and Hussaini, M. Y. (1981). Mixed spectral-finite difference approximations for slightly viscous flows, inLecture Notes in Phys., No. 141, Proc. of the 7th Intl. Conf. on Numerical Methods in Fluid Dynamics, Reynolds, W. C., and MacCormack, R. W., (eds.), Springer-Verlag.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kopriva, D.A. A practical assessment of spectral accuracy for hyperbolic problems with discontinuities. J Sci Comput 2, 249–262 (1987). https://doi.org/10.1007/BF01061112
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01061112