A Crank-Nicolson discontinuous Galerkin pressure-projection method for the hydrodynamic and sediment transport model

In this article, we construct and analyze a second-order time-accurate, linear, decoupled fully-discrete discontinuous Galerkin (DG) pressure-projection numerical scheme for the hydrodynamic and sediment transport model. The proposed algorithm is based on DG method for spatial discretization, Crank-Nicolson (C-N) scheme for temporal discretization, linearly extrapolated scheme for the nonlinear term and coupling term and pressure-projection method for the Navier-Stokes equations. Moreover, we rigorously prove the unconditional stability and optimal error estimates of the proposed fully-discrete scheme. We make use of the techniques developed by Pietro et al. to prove the optimal error estimates for pressure rigorously. Finally, several numerical examples are performed to numerically demonstrate the accuracy, efficiency and applicability of the proposed scheme.