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In this paper we propose a novel arbitrary high order accurate semi-implicitspace-time discontinuous Galerkin method for the solution of the twodimensional incompressible Navier-Stokes equations on staggered unstructuredtriangular meshes. Isoparametric finite elements are used to take into accountcurved domain boundaries. The discrete pressure is defined on the primaltriangular grid and the discrete velocity field is defined on an edge-basedstaggered dual grid. While staggered meshes are state of the art in classicalfinite difference approximations of the incompressible Navier-Stokes equations,their use in the context of high order DG schemes is novel and still quiterare. Formal substitution of the discrete momentum equation into the discretecontinuity equation yields a sparse four-point block system for the scalarpressure, which is conveniently solved with a matrix-free GMRES algorithm. Avery simple and efficient Picard iteration is then used in order to achievehigh order of accuracy also in time, which is in general a non-trivial task inthe context of high order discretizations for the incompressible Navier-Stokesequations. The flexibility and accuracy of high order space-time DG methods oncurved unstructured meshes allows to discretize even complex physical domainswith very coarse grids in both, space and time. The use of a staggered gridallows to avoid the use of Riemann solvers in several terms of the discreteequations and significantly reduces the total stencil size of the linear systemthat needs to be solved for the pressure. The proposed method is validated forapproximation polynomials of degree up to $p=4$ in space and time by solving aseries of typical numerical test problems and by comparing the obtainednumerical results with available exact analytical solutions or other numericalreference data.

A staggered space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations on two-dimensional triangular meshes