A new method for the rapid solution, including set-up, of incompressible flow over complex bodies is presented. The method treats the body surface as well as shed vorticity as a set of vortex sheets or filaments embedded in a regular, fixed, non-conforming Cartesian grid and is completely Eulerian, requiring no separate markers or other Lagrangian components. This method represents a very simple, economical way to treat complex bodies since it does not require grid generation and can use of a fast Cartesian grid flow solver. It allows the computation of thin convecting vortices over arbitrarily long distances with no numerical spreading. It also automatically allows the general separation, linking and other types of interactions of convecting vortical regions. The method is based on a technique known as "Vorticity Confinement" that involves adding a simple term to the Navier-Stokes equations. When discretized and solved, these modified equations admit convecting, concentrated vortices that maintain a fixed size and do not spread, even if there is numerical diffusion. Also, if a complex body surface is described by the zero contour of a smooth scalar "level set" function, which is defined on each point of a regular Cartesian computational grid, the flow over the body surface can be solved with a no-slip boundary condition imposed. The Vorticity Confinement method effectively confines the vorticity to a thin region surrounding the body surface (zero contour), as well as thin regions of convecting, shed vorticity, even on a coarse computational grid and with low order discretization schemes. Unlike other general Cartesian grid methods, no special logic is needed to determine the body surface in the present method. Also, the vorticity can be shed from smooth surfaces as well as surfaces with sharp corners.
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