An edge-based method for the incompressible Navier-Stokes equations on polygonal meshes

A pressure-based method is presented for discretizing the unsteady incompre ssible Navier-Stokes equations usings hybrid unstructured meshes. The edge- based data structure and assembly procedure adopted lead naturally to a str ictly conservative discretization, which is valid for meshes composed of n- sided polygons. Particular attention is given to the construction of a pres sure-velocity coupling procedure which is supported by edge data, resulting in a relatively simple numerical method that is consistent with the bounda ry and initial conditions required by the incompressible Navier-Stokes equa tions. Edge formulas are presented for assembling the momentum equations, w hich are based on an upwind-biased linear reconstruction of the velocity fi eld. Similar formulas are presented for assembling the pressure equation. T he method is demonstrated to be second-order accurate in space and time for two Navier-Stokes problems admitting an exact solution. Results for severa l other well-known problems are also presented, including lid-driven cavity flow, impulsively started cylinder flow, and unsteady vortex shedding from a circular cylinder. Although the method is by construction minimalist, it is shown to be accurate and robust for the problems considered. (C) 2001 A cademic Press.