Experimental Report on Establishing Numerical Solution Characteristics for the NS Equations

When solving the Navier - Stokes (NS) equations, the Finite Volume Method (FVM), although with high accuracy, has the problems of cumbersome calculation and long time consumption. For example, detecting a shock wave often takes several days. In order to quickly explore the characteristics of the numerical solutions of the NS equations, this experiment uses a multi - scale regional adaptive sampling method to obtain the numerical points of the local approximate solutions of the NS equations. Then, combined with the Fast Fourier Transform (FFT) and Wavelet Transform, the sequences of velocity components , , and  are analyzed to quickly detect the frequency and multi - scale characteristics of the solutions. The experimental results show that this method can efficiently reveal the dynamic behavior of the solutions of the NS equations and provide a convenient analysis approach for subsequent related research.