A numerical scheme to solve the two-dimensional Euler equations around aerodynamic profiles is presented. The space domain is discretized by an unstructured mesh where triangular elements are used. The scheme uses a first- and a second-order finite volume method where evolution equations for the mean values are obtained at each cell. The first-order approximation is obtained by a constant approximation at each cell while the second-order approximation is obtained by a linear ENO (essentially non-oscillatory) polynomial. Fluxes at cell interfaces are determined using an approximate solver for the Riemann problem. The solution of the Riemann problem introduces the upwind characteristic of the scheme.
In this paper, particular emphasis is placed on the determination of fluxes at every cell interface, obtaining a compact expression for the resolution on unstructured meshes. The Burgers equation is analysed as a typical scalar case, and it is shown how the vectorial Riemann problem in unstructured meshes can be reduced to four scalar problems along four directions of propagation. This paper also shows how the use of a preconditioned technique based on local time step improves the convergence to the steady state solution. An anomalous behaviour in the convergence of the residuals in a second-order scheme is observed and it is related to the shock structure and the spatial approximation. Transonic and subsonic test cases of aerodynamic profiles are simulated as an application to advanced aerodynamic design.
Essentially non-oscillatory schemes for the Euler equations on unstructured meshes
1999-01-01
12 pages
Article (Journal)
Electronic Resource
English
Essentially non-oscillatory schemes for the Euler equations on unstructured meshes
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