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A high-order discontinuous Galerkin method for 2D incompressible flows. (English) Zbl 0963.76069
Conclusions: We present a high-order discontinuous Galerkin method for two-dimensional incompressible Euler and Navier-Stokes equations in vorticity-streamfunction formulation, coupled with a standard continuous finite element solution of Poisson equation for the streamfunction. A natural matching between the two finite element spaces allows us to obtain total energy conservation and total enstrophy stability. Numerical examples are shown to demonstrate the accuracy and resolution of the method, and to verify optimal error estimates.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M10 Finite element methods applied to problems in fluid mechanics
76B99 Incompressible inviscid fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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