Unconditionally energy-stable discontinuous Galerkin method for the chemo-repulsion-Navier-Stokes system

In this paper, we derive a chemo-repulsion-Navier-Stokes system, which can be used to describe the chemo-repulsion movement of microorganisms in the incompressible fluid. An efficient fully discrete scheme is proposed for solving this chemotaxis-fluid system. The novelty of the proposed scheme is a linear and decoupled structure, which is constructed by using the discontinuous Galerkin (DG) method for spatial discretization, the implicit -explicit (IMEX) approach for the highly nonlinear and coupling terms, and a pressure-projection method for the Navier-Stokes equations. The unconditionally energy stability and the optimal error estimates of the developed scheme are proved strictly. Finally, some numerical examples are provided to demonstrate the accuracy, energy stability and the performance of the proposed numerical scheme.