Application of a generalized multiphase Riemann solver to a finite-volume method with nozzling sources

Abstract

Abstract. Hyperbolic model equations governing the flow of solid particles within a gas contain nonconservative nozzling sources that can introduce numerical artifacts in commonly used finite-volume methods. Modifications to these techniques have been recently proposed, involving both exact and approximate solutions to the two-phase Riemann problem with gamma-law equations of state. The present work extends this approach to solid phases characterized by general equations of state. An exact Riemann solver is formulated within the context of the second-order, semidiscrete, cell-centered Kurganov-Tadmor (KT) finite-volume method. The resulting scheme may be used to predict wave structures and energetics for 1D piston-impact of mixtures having large initial spatial variations in volume fraction, where the physical effects of nozzling are more significant. It is shown that neglecting a class of wave configurations arising in the Riemann problem, as practiced in the literature, can lead to nonphysical solutions. A framework for the analysis of Riemann problems including an arbitrary number of solid phases is also discussed.