Computation of flows with arbitrary equations of state

The extension of time-marching computations to fluids with arbitrary equations of state is demonstrated by means of stability analyses, simplified problems, and practical applications. Most of the examples use the properties of supercritical hydrogen for which the density varies by more than an order of magnitude for small changes in pressure and temperature, but representative computations for incompressible fluids and perfect gases are also given to demonstrate the generality of the procedure. Because representative how velocities in typical supercritical fluids applications are much lower than the speed of sound, convergence enhancement through eigenvalue control is often necessary. This is accomplished through a generalization of earlier preconditioning methods that enables efficient computation of arbitrary equation of state fluids, perfect gases, and incompressible fluids by a single procedure. The present approach thus provides a single method that is uniformly applicable to all equations of state.