Spectral element-FCT method for the one- and two-dimensional compressible Euler equations

✍ Scribed by John G. Giannakouros; David Sidilkover; George Em Karniadakis

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 471 KB
• Volume: 116
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(94)80014-6

✦ Synopsis

A hybrid spectral element-FCT method is proposed for the solution of the Euler equations of gas dynamics in one and two space dimensions. It is based on a new conservative formulation starting from standard spectral method expansions and incorporating ideas of modern finite volume schemes. A staggered mesh is employed in the discretization, consisting of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points for the calculation of averaged quantities and fluxes, respectively. Use of limiting is based on the flux-corrected transport algorithm. The outcome Is a geometrically flexible scheme with optimal phase properties. Both one-and two-dimensional results are presented, in which the Gibbs phenomenon is absent while all transition zones are exceptionally sharp.