Numerical analysis of a chemotaxis-swimming bacteria model on a general triangular mesh

This paper is devoted to the numerical study of a model arising from biology, consisting of chemotaxis equations coupled to Navier-Stokes flow through transport and external forcing. A detailed convergence analysis of this chemotaxis-fluid model by means of a suitable combination of the finite volume method and the nonconforming finite element method is investigated. In the case of nonpositive transmissibilities, a correction of the diffusive fluxes is necessary to maintain the monotonicity of the numerical scheme. Finally, many numerical tests are given to illustrate the behavior of the anisotropic Keller-Segel-Stokes system.