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A spectral element-FCT method for the compressible Euler equations. (English) Zbl 0811.76058
A new algorithm based on spectral element discretizations and flux- corrected transport (FCT) concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss- Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one and two dimensions. It is demonstrated through shock- tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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