Eulerian consistent smoothed particle hydrodynamics (SPH) method for weakly compressible viscous flows applied to lid-driven cavity

In this study, nonlocal gradient and divergence operators are introduced to eliminate the dependence on the derivation of the kernel function in smoothed particle hydrodynamics (SPH) and improve the numerical stability and interpolation consistency. Eulerian consistent SPH equations for weakly compressible viscous flows are derived, and a new laminar viscosity model is proposed. Several benchmark problems were reproduced using the developed code, demonstrating the accuracy of the proposed method. Finally, this method was applied to simulate a lid-driven cavity problem at different Reynolds numbers (Re). The results obtained were compared with those of the existing literatures, exhibiting good consistency and demonstrating its reliability in viscous flows simulation.