This work aims to study the interaction of a shock wave with a cloud of particles to quantify flow unsteadiness and velocity fluctuations using particle-resolved direct numerical simulation (PR-DNS). Three cases are studied, with each case revealing one aspect of the intricate flow phenomena involved in this interaction. The unsteady interaction of a shock wave with a transverse array of particles reveals the origin of unsteadiness under the effect of mutual wave-wave and wave-wake interactions between the particles. In the second case, the interaction of a shock with a particle cloud is studied, with a focus on the interaction of the complex wave system with the vortical structure. A budget analysis of the vorticity equation reveals the sources of strong unsteadiness in the particle cloud. A detailed analysis of the velocity fluctuation and kinetic energy in the fluctuating motion is performed to ascertain the importance of the velocity fluctuations that arise from the strong unsteadiness. An analogous analysis is presented, in the third case, for a gradually-induced flow on the same particle cloud along with a comparison to the shock induced case to assess the impulsive effect of shock on intensity of the fluctuating field statistics.

This paper describes the extension of the simple low-dissipation AUSM (SLAU) scheme to a six-equation compressible two-fluid model for gas/liquid flow. This is the latest version of the AUSM-family of schemes with a new numerical flux function. This scheme features low dissipation without any tunable parameters in low Mach number regimes while maintaining the robustness of the AUSM-family fluxes at high Mach numbers with a very simple formulation. The accuracy of the method is tested with a well-known two-fluid air/water flow benchmark problem and the results were compared with the two-phase AUSM + and AUSM + -up schemes.Accurate methods to simulate multiphase flows are necessary to model engineering applications. Modern commercial solvers employ a range of methods, such as the mixture model, volume-of-fluid model, or the EulerEuler two-fluid approach 1,2 . These approaches are generally pressure-based and assume incompressibility of the liquid phase. However, because of their limited accuracy, as well as inability to model strong compressibility effects, the current generation of two-phase flow schemes are density-based. Furthermore, these algorithms can be problematic because the governing equations contain nonhyperbolicity, nonconservative form, and numerical stiffness from the large disparity in fluid properties and flow scales 3 . On the other hand, in the density based solvers, either for single or two-phase flow, special care must be taken to prevent slow or stalled convergence, which can occur from the large ratio of characteristic speeds and errors arising from excessive amounts of numerical dissipation 4 .The AUSM (Advection Upstream Splitting Method), originally developed by Liou and Steffen 5 , and its variant AUSM-family schemes are known to be excellent at resolving flow discontinuities while remaining computationally inexpensive and not requiring characteristic analysis or field by field decomposition 6 . Thus, they have been widely used as one of the standard methods of compressible CFD algorithms, especially when dealing with non-hyperbolic models, or with models whose mathematical properties depend closely on closure laws as in two-phase flow. This scheme has been employed successfully by several authors to simulate multiphase flow in different test cases 7,8,9,10,11 . Recently, all-speed versions of the AUSM-family of schemes have been developed that can be used for low to high Mach number flows 12 . However, these schemes include at least one problem-dependent parameter, such as the cut-off Mach number. This parameter should be a very small but non-zero number for very low Mach number flows. The approach can be problematic since there is no proper method to define the cut-off Mach number, especially when no uniform flow is present 4,13 .Recently, a new, simple low-dissipation numerical flux function of the AUSM-family has been developed 4,13 for all speeds, called the simple low-dissipation AUSM (SLAU). In contrast with previous all-speed schemes, the simple low-dissipation AUSM features low d...