Fluctuation Splitting Schemes for the Compressible and Incompressible Euler and Navier-Stokes Equations

Introduced in the late eighties by Roe, fluctuation splitting (or residual distribution) schemes have recently emerged as a viable alternative to Finite Volume and Finite Element methods for PDE based, fluid dynamics simulations using unstructured meshes. Their application to the numerical approximation of the compressible and incompressible Euler and Navier-i Stokes equations is described, emphasizing low Mach number and incompressible applications. The advantages provided by time-preconditioning techniques are discussed and details of the implementation are given.