Analysis of Dynamical Structure by Considering the Randomness of Insertion of Errors and Development for Numerical Analysis on Conservative System

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In this research, we considered the dependence of the numerical simulation results on inserted randomness. We adopted compressible fluid equations as calculation models. It is difficult to apply the statistical approach to the conservative system because it is structurally unstable. We calculated the statistical data of position of fluctuating shock wave induced by the forcibly added randomness in order to investigate the dependence of simulation results on the random errors. When the amplitude of randomness becomes relatively large, it is clarified that the mean position of shock wave moves toward leeward region. On the other hand, we showed that the forcibly added randomness affects the bifurcation process in the case of dissipative system. These results obtained in the present research give researchers significant information about the dependence of reliability of numerical results on random erros.