A semi‐implicit stabilized particle Galerkin method for incompressible free surface flow simulations.

Summary: A new particle Galerkin method is introduced to solve the Naiver‐Stokes equations in a Lagrangian fashion. The present method aims to suppress key numerical instabilities observed in the strong form Lagrangian particle methods such as smoothed particle hydrodynamics (SPH), incompressible SPH, and moving particle semi‐implicit for incompressible free surface flow simulations. It is well‐known that strong form Lagrangian particle methods usually rely on ad hoc particle stabilization techniques based on particle shifting, artificial viscosity, or density‐invariant condition due to some formulation inconsistency issues. In the present method, we introduce a momentum‐consistent velocity smoothing algorithm which is used to combine with the second‐order rotational incremental pressure‐correction scheme to stabilize the pressure field as well as to enforce the consistency of Neumann boundary condition. To further impose slip‐free or nonslip boundary conditions for the fluid flow, a penalty method which is free of ghost or dummy particles is developed. Finally, a particle insertion‐deletion adaptive scheme is proposed when the violent fluid flow is considered. Four numerical examples are studied to validate the accuracy and stability of the present method. [ABSTRACT FROM AUTHOR]