High-order velocity and pressure wall boundary conditions in Eulerian incompressible SPH

Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator

“…In many particle-based methods, the pressure field can be obtained by solving the pressure Poisson equation. This pressure field is then used to correct the velocity field to make it divergence-free (Fourtakas et al, 2018;Hosseini and Feng, 2011;Lind and Stansby, 2016;Nasar et al, 2020;Shadloo et al, 2012;Shao and Lo, 2003;Solenthaler and Pajarola, 2009).…”

“…In a discretized model, to obtain the Eulerian form of the pressure Poisson equation, first, the continuity and momentum equations given in Eq. ( 2) for incompressible fluid is written in the numerical form as (Fourtakas et al, 2018;Lind and Stansby, 2016;Nasar et al, 2020)…”

“…First, the pressure field at time 𝑡 is obtained by solving the pressure Poisson equation given in Eq. ( 7) (Fourtakas et al, 2018;Hosseini and Feng, 2011;Lind and Stansby, 2016;Nasar et al, 2020;Shadloo et al, 2012;Shao and Lo, 2003;Solenthaler and Pajarola, 2009). The pressure is subjected to boundary conditions described in Section 4.…”

Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling

“…This test case was somewhat idealized in being periodic and without solid walls, which, at the time, were only available to be at best second-order accurate and, therefore, disruptive to ideal high-order convergence. This restriction is being resolved, however, with promising high-order boundary conditions being developed that are able to model internal wall-bounded flows, also in Eulerian form [123]. This new approach provides high-order approximations to no-slip and no-flux boundary conditions allowing globally high-order solutions to the Navier–Stokes equations (see, for example, the Taylor–Couette flow and convergence plots shown in figure 5).…”

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

“…On the other hand, an alternative way to compute the WENO reconstruction polynomials is proposed: the MLS fits used in [31] have been replaced with a corrected SPH interpolation [22] with the aim of remarkably improving the efficiency of the numerical scheme. Though boundary conditions are not included in the declared scope of this work, a high-order boundary treatment is also required to achieve global high order convergence of the scheme, as demonstrated for the case of Eulerian SPH [36]. For the implementation, the DualSPHysics open-source project [37] has been chosen as baseline for its efficiency and capability of exploiting the computational power of modern graphics processing units (GPUs).…”