Applying Riemann solvers to open boundaries in free surface and confined flows

Due to the Lagrangian nature of SPH, dealing with open boundaries (which are intrinsically Eulerian) is a challenging issue. This issue has recently been addressed in the Unified Semi-Analytical Boundaries framework [1], where it has been shown how to properly deal with mass fluxes at the open boundaries. However imposing both velocities and pressures on the open boundaries will over-constrain the problem, and in most cases only one of these quantities will be known. Therefore, Riemann Solvers can be used to calculate and prescribe compatible fields at the open boundaries. These compatible fields allow therefore complex boundary conditions to be imposed.