An immersed boundary method for compressible multiphase flows: application to the dynamics of pyroclastic density currents

An immersed boundary technique suitable for the solution of multiphase compressible equations of gas-particle flows of volcanic origin over complex 2D and 3D topographies has been developed and applied. This procedure combines and extends different existing methods designed for incompressible flows. Furthermore, the extension to compressible multiphase flows is achieved through a flux correction term in the mass continuity equations of the immersed cells that accounts for density variations in the partial volumes. The technique is computationally accurate and inexpensive, if compared to the use and implementation of the finite-volume technique on unstructured meshes. The first applications that we consider are the simulations of pyroclastic density currents generated by the collapse of a volcanic column in 2D axisymmetric geometry and by a dome explosion in 3D. Results show that the immersed boundary technique can significantly improve the description of the no-slip flow condition on an irregular topography even with relatively coarse meshes. Although the net effect of the present technique on the results is difficult to quantify in general terms, its adoption is recommended any time that cartesian grids are used to describe the large-scale dynamics of pyroclastic density currents over volcano topographies.