Abstract
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.
Highlights
The shallow water equation is one of the macrogoverning equations that are commonly used in hydraulic simulation
Based on the research of Leveque, Xu, and others, the results in this paper have shown that the number of grids in the simulation should be within a reasonable range when the large time step (LTS) scheme is implemented
Leveque utilized the random choice method (RCM) in his research in order to suppress any oscillation in the LTS scheme, residual oscillation still occurred at the discontinuity
Summary
The shallow water equation is one of the macrogoverning equations that are commonly used in hydraulic simulation. It adopts a nonlinear filter factor to process the numerical solution at each time step, and it only acts on part of the grid points; the computational efficiency is relatively high This method only works on short waves and only has a small effect on long waves. The RCM and nonlinear filter from aeroacoustics have been combined to achieve the effect of suppressing the numerical oscillation at the discontinuity generated by the LTS scheme. Before this combination of methods was conducted, the random sequence combination in the RCM was statistically analyzed, and error analysis was performed to optimize the combination of sequences that is appropriate for the RCM. USING THE LTS SCHEME TO SOLVE THE GOVERNING EQUATION OF THE ONE-DIMENSIONAL SHALLOW WATER EQUATION
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