A critical comparison of two discontinuous galerkin methods for the navier-stokes equations using solenoidal aproximations
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This paper compares two methods to solve incompressible problems, in particular the Navier-Stokes equations, using a discontinuous polynomial interpolation that is exactly divergence-free in each element. The first method is an Interior Penalty Method, whereas the second method follows the Compact Discontinuous Galerkin approach for the diffusive part of the problem. In both cases the Navier-Stokes equations are then solved using a fractional-step method, using an implicit method for the diffusion part and a semiimplicit method for the convection. Numerical examples compare the efficiency and the accuracy of the two proposed methods.