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An accuracy assessment of Cartesian-mesh approaches for the Euler equations. (English) Zbl 0817.76055
A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations is made. An exact solution of the Euler equations (Ringleb’s flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different \(K\)-exact reconstruction procedures.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76H05 Transonic flows
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