A kernel gradient-free SPH method with iterative particle shifting technology for modeling low-Reynolds flows around airfoils

The conventional SPH method does not perform well for simulating flows around rigid bodies. Especially, it is difficult to get convergent and accurate results when simulating flows around a thin airfoil. The reason is its low accuracy especially for highly irregular particle distributions in the process of SPH simulation of flow around slender structures. In this paper, a kernel gradient-free (KGF) SPH method with iterative particle shifting technology (PST) is proposed for the simulation of flow around the airfoil. KGF-SPH can maintain high accuracy without using kernel gradients. Iterative PST can maintain uniform particle distribution even if the smoothing length is less than the average particle spacing. Lid-driven shear cavity flows, Taylor-Green flow, the stretching of a free-surface circular fluid patch and flows around a cylinder are simulated to test the numerical method. Numerical results are almost in consistent with the analytical or reference results. Finally, flows past an airfoil are simulated by using the proposed SPH method. The results show that the present SPH method effectively improves numerical stability and accuracy for simulating flows around an airfoil.