A High Order Discontinuous Galerkin Method for 2D Incompressible Flows
نویسندگان
چکیده
In this pat)er we introduce a high order discontinuous Galerkin method for two dimensional incoinpressible flow in vorticity streamfunction fornnllation. The inonlentuni equation is treated exl)licitly, utilizing the efficiency of the discontimtous Galerkin method. The streanlflmction is obtained by a standard Poiss(m solver using (:ontinu(lus finite elenmnts. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element I)oundaries. This allows for a correct upwinding ghting ill the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation aim total enstrophy stability. The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by immerical experinmnts. Key words, incompressible flow, discontinuous Galerkin, high order accuracy Subject classification. Apt)lied and Numerical Mathematics
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