Well-balanced open boundary condition in a lattice Boltzmann model for shallow water with arbitrary bathymetry

In this paper we propose a new method for the treatment of open boundary condition for lattice Boltzmann method applied to the shallow water simulations in a D2Q9 mesh. We also prove the accomplishment of the well-balanced property for the proposed model. This analysis is done for an arbitrary node in the domain and several boundary conditions. We validate our model through several numerical tests, including a lake at rest and cylindrical dam break flows over flat and complex bathymetries. The numerical simulation shows that our proposal for open boundary condition retains the main features of the waves when crossing such boundaries.