SPECTRAL ELEMENT FCT METHOD FOR THE ONE-DIMENSIONAL AND 2-DIMENSIONALCOMPRESSIBLE EULER EQUATIONS

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