Non-Oscillatory Central Schemes for the Incompressible 2-D Euler Equations

We adopt a non-oscillatory central scheme, first presented in the context of Hyperbolic conservation laws in [28] followed by [15], to the framework of the incompressible Euler equations in their vorticity formulation. The embedded duality in these equations, enables us to toggle between their two equivalent representations -- the conservative Hyperbolic-like form vs. the convective form. We are therefore able to apply local methods, to problems with a global nature. This results in a new stable and convergent method which enjoys high-resolution without the formation of spurious oscillations. These desirable properties are clearly visible in the numerical simulations we present. AMS(MOS) subject classification. Primary 65M10; Secondary 76C05 Keywords. Hyperbolic conservation laws, second-order accuracy, central difference schemes, nonoscillatory schemes, Incompressible Euler equations. 1 Introduction We are concerned with the approximate solution of fluid flows governed by the follow..