A high-order, conservative Eulerian method is presented for the simulation of vortex dominated inviscid fluid flows. The primitive variable incompressible Euler equations are recast in the velocity-vorticity form to explicitly enforce conservation of vorticity. The advection of the vorticity is then calculated via a two-step process: the velocity field is determined by evaluation of the Biot-Savart integral, and then a line-based discontinuous Galerkin (DG) Eulerian spatial discretization scheme is applied to accurately advect the vorticity field. The accuracy and convergence of this method was examined for test cases where an analytical solution exists, as well as more challenging test cases which lack an analytical solution. The convergence rate behavior is chiefly controlled by the error in the calculated velocity field. Velocity errors are due to two factors: the approximation of the Biot-Savart integral with a desingularized form, and reduced quadrature convergence for the nearly singular integral. Solver parameters were chosen to balance these two effects resulting in nearly optimal convergence of the overall method in the analytical test, and high-order convergence in the qualitative test case.
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