Numerical flux function for flow through porous media with discontinuous properties

Highlights: • A new numerical flux function is developed for interface between porosity changes. • The flux function can be easily implemented into existing flow solvers. • Accurately captures the behavior of finite waves interacting with area changes. • Good agreement with experimental flow over transpiration cooling porous plate. -- Abstract: A numerical flux function is developed for handling the flow across a porosity interface. The flux function is based on an idealization of the interface between volumes of different porosity as a sudden area change, intervening over a layer of negligible thickness. The evaluation of numerical fluxes at the interface uses any numerical flux function for the Euler equations but applied to sets of variables that keep into account the area change and the conditions on either side of the interface. The new flux function is compared to analytical solutions of the interaction of waves of finite amplitude with an area change. Excellent agreement is shown between the analytical solutions, a standard quasi-one-dimensional solution with an area change over a finite length, and the new flux function. Due to its simplicity, the proposed flux function can be easily introduced into existing multi-dimensional solvers. The new flux function is applied to a transpiration cooling problem and compared to other results in literature. Good agreement with published experimental results is shown. The flux function provides an efficient means of handling the porosity interfaces and obviates the need for any coupling of porous and free flow solvers.