A Velocity Correction Projection Method Based on Pressure Filtering Finite Element Format

Based on the finite element formulation and guided by the principle that pressure discretization is one order lower than velocity discretization, this study introduces a pressure-filtered velocity-correction projection method by applying a low-order filtering strategy to the pressure field obtained from the traditional velocity-correction projection method. Numerical results demonstrate that the improved method effectively suppresses the occurrence of pressure oscillations compared to the conventional approach. Further analysis reveals the underlying mechanism of pressure oscillations and shows that such oscillations become increasingly prominent as the time step size decreases, attributed to the amplification of velocity divergence errors in the source term of the pressure Poisson equation. This work provides a robust framework for stabilizing pressure solutions in small-time-step simulations and offers theoretical insights for error control in projection-based algorithms.