An efficient second-order filtered characteristic method for Navier–Stokes equations with its adaptive optimization

This paper delves into the applications of the characteristic method (CM) and the time filter (TF) in the numerical resolution of the Navier–Stokes equations. To improve the temporal accuracy from first to second order without significantly increasing the computational complexity, the TF is appended to the original first-order CM. Subsequently, we also find that this method facilitates the construction of adaptive algorithms. Through rigorous numerical experiments and in-depth result analyses, the merits of combining the characteristic method with time filter in enhancing computational precision and efficiency are corroborated.