Numerical Analysis of Dusty-Gas Flows

High‐Resolution Finite Volume Methods for Dusty Gas Jets and Plumes

“…The pressure ϕ associated to the dispersed phase is small in comparison to the gas pressure p g , and considering negligible interaction between particles (droplets), it can be assumed to be zero, as in [17,43]. However, a nonzero ϕ plays an important role from a mathematical point of view, since the homogeneous equations of the dispersed phase lose strict hyperbolicity under the hypothesis ϕ ≡ 0.…”

“…They can be neglected, as in [43]. These nonconservative terms pose a mathematical difficulty when we wish to allow for discontinuous solutions of the two-phase system.…”

“…In section 7.1 we consider a one-dimensional test with no gravity taken from [43]. In section 7.2 we report results of two-dimensional computations including gravity effects in the context of simulation of volcanic processes.…”

“…We simulate a shock tube experiment that has been studied numerically by Saito in [43] and was originally considered in [31]. It involves high-pressure and high-density pure air (γ = 1.4) in the driver section and air laden with solid particles at room conditions in the driven section.…”

“…The formulation that we adopt to describe the dynamics of this two-phase flow under the above assumptions follows especially the work of Harlow and Amsden [17], Sainsaulieu [40,42,41], and Saito [43]. In particular, the physical and numerical model in [17] has been widely used in the field of geophysics to study the particle-laden flows ejected during volcanic eruptions, e.g., [46,44,10,32,36,9].…”