On discontinuous solutions of hyperbolic equations

✍ Scribed by Knut S. Eckhoff

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 642 KB
• Volume: 116
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(94)80013-8

✦ Synopsis

A modified Fourier method which is applicable to numerical simulations of discontinuous solutions of hyperbolic equations is presented. Truncated Fourier series representations are de-truncated at every timestep by utilising step-functions in the reconstruction of the discontinuous solutions. The de-truncated expansions are used to eliminate the numerical dispersion and diffusion which normally ruin the discontinuous solutions in a few timesteps when traditional Fourier methods are applied.