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Symmetry techniques for the numerical solution of the 2D Euler equations at impermeable boundaries. (English) Zbl 0918.76055
Summary: We consider the implementation of boundary conditions at rigid, fixed wall boundaries in inviscid Euler solutions by upwind, finite volume methods. Some current methods are reviewed. Two new boundary condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique, are then presented. Their behaviour in relation to the problem of the subsonic flow about blunt and slender elliptic bodies is analyzed, and the subsonic flow inside the Stanitz elbow is computed. The symmetry technique is proven to be as accurate as one of the current methods, second-order pressure extrapolation technique. Finally, for arbitrary curved geometries, we show dramatic advantages of the curvature-corrected symmetry technique over other methods.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76G25 General aerodynamics and subsonic flows
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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