The numerical oscillation suppression method for the large time step scheme

The large time step scheme, which is commonly used in hydrodynamic numerical simulation, adopts the multielement reconstruction method in order to improve both the computational efficiency and accuracy; however, this results in numerical oscillation and calculation divergence. Therefore, it is necessary to develop methods to suppress the occurrence of numerical oscillation near the discontinuities. The numerical oscillation that is induced can be suppressed by using the random choice method (RCM) with the van der Corput random number sequence. In order to optimize the suppression performance, error analysis has been carried out in this paper for the calculation results from the RCM with the popular van der Corput random sequence combinations for selecting the optimal sequence combination. In order to further eliminate any short-wave numerical oscillations near the discontinuities, a method that combines the RCM with a nonlinear filter, which often used in aeroacoustic calculations, has been proposed in this paper to suppress short-wave oscillations. Specifically, the RCM and the nonlinear filter method were sequentially implemented in order to process the calculation results at each time step. The results showed that this method had a good suppression effect on the numerical oscillations near the discontinuities, which was demonstrated by the numerical experiments.