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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.

MSC:
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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