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| Through the preliminary numerical calculations, we gained confidence on the use of the NNDschemes, the principle of choice of the coefficients of the third order derivatives is still based on the linearized conclusion. Under the unsteady, nonlinear conditions, the validate is an open question. Symmeries could help us to reach a new conlusion, which domenstrated that the linearized conclusion is met with the similarity inavirants, but not for the Galileo invariants in general case. In this paper, the spatial oscillations in finite difference solutions for Navier-Stokes shocks are re-explored from a point view of group-invariance theory. It is shown that the oscillations of numerical solutions in the upstream and downstream regions of shock have link with the symmetry broken. The symmetry inherent necessary conditions must be satisfied for the choice of finite difference schemes. |
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| Keywords:shock capturing method; symmetries; NND schemes. |
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