Consistency analysis of flow field extension models into ghost fluid regions for SPH solid body boundary condition implementations

In the present paper, the consistency of continuous SPH approximations to the differential operators appearing in the Navier-Stokes system is analyzed. In particular, emphasis is made on the consistency of such operators when evaluated close to the boundaries of the fluid domain and flow extension techniques are applied. The divergence of the velocity field, the pressure gradient and the velocity Laplacian, present in Navier-Stokes equations, are considered. The question of how the extension scheme used in each field, both velocity and pressure, may affect the accuracy of the SPH approximation of differential operators close to the boundaries is addressed. An answer to this question is given by means of consistency arguments based on analytical tools.