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

We adopt a non-oscillatory {\it central} scheme, first presented in the context of Hyperbolic conservation laws in \cite{nessyahu-tadmor:non-oscillatory} followed by \cite{jiang-tadmor:nonosc}, 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.

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Published 1 January 1997