Compressible and incompressible limits for hyperbolic systems with relaxation

A general relaxation system which yields compressible and incompressible Euler and Navier–Stokes equations in the limit is presented. Such a system can be used to set up relaxation schemes that work uniformly in the above limits. A higher order nonoscillatory upwind spatial discretization and TVD implicit–explicit method for time integration are considered. Numerical computations are carried out on various test problems.