Hyperbolic-Elliptic Splitting for the Pseudo-Compressible Euler Equations

Following previous work on the canonical decomposition of the subsonic, compressible Euler equations into their steady hyperbolic and elliptic components, a similar decomposition for the incompressible equations is proposed. The artificial compressibility approach is used make the incompressible Euler equations hyperbolic in time. The canonical form of this pseudo-compressible system consists in an hyperbolic component corresponding to the convection of total pressure along the streamlines and a Cauchy-Riemann system corresponding to the omni-directional propagation of the (artificial) acoustic waves. The discretization of the pseudo-unsteady system is accomplished using Fluctuation Splitting schemes and unstructured meshes.