Preconditioned methods for simulations of low speed compressible flows

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid compressible flow at low speeds is formulated. The preconditioned system of equations are hyperbolic in time and remain well-conditioned in the incompressible limit. The preconditioning formulation is easily generalized to multicomponent/multiphase mixtures. When applying conservative methods to multicomponent flows with sharp fluid interfaces, nonphysical solution behavior is observed. This stimulated the authors to develop an alternative solution method based on the nonconservative form of the equations which does not generate the aforementioned nonphysical behavior. Before the results of the application of the nonconservative method to multicomponent flow problems is reported, the accuracy of the method on single component flows will be demonstrated. In this report a series of steady and unsteady inviscid flow problems are simulated using the nonconservative method and a well-known conservative scheme. It is demonstrated that the nonconservative method is both accurate and robust for smooth low speed flows, in comparison to its conservative counterpart.