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A new high order accurate semi-implicit space-time Discontinuous Galerkinmethod on staggered grids, for the simulation of viscous incompressible flowson two-dimensional domains is presented. The designed scheme is of theArbitrary Lagrangian Eulerian type, which is suitable to work on fixed as wellas on moving meshes. In our space-time formulation, by expressing the numericalsolution in terms of piecewise space-time polynomials, an arbitrary high orderof accuracy in time is achieved through a simple and efficient method of Picarditerations. For the dual mesh, the basis functions consist in the union ofcontinuous piecewise polynomials on the two subtriangles within thequadrilaterals: this allows the construction of a quadrature-free scheme,resulting in a very efficient algorithm. Some numerical examples confirm thatthe proposed method outperforms existing ones.

A semi-implicit high-order space-time scheme on staggered meshes for the 2D incompressible Navier-Stokes equations