Numerical simulation of pyroclastic density currents using locally refined Cartesian grids

Pyroclastic density currents are ground hugging, hot, gas–particle flows representing the most hazardous events of explosive volcanism. Their impact on structures is a function of dynamic pressure, which expresses the lateral load that such currents exert over buildings. Several critical issues arise in the numerical simulation of such flows, which involve a rheologically complex fluid that evolves over a wide range of turbulence scales, and moves over a complex topography. In this paper we consider a numerical technique that aims to cope with the difficulties encountered in the domain discretization when an adequate resolution in the regions of interest is required. Without resorting to time-consuming body-fitted grid generation approaches, we use Cartesian grids locally refined near the ground surface and the volcanic vent in order to reconstruct the steep velocity and particle concentration gradients. The grid generation process is carried out by an efficient and automatic tool, regardless of the geometric complexity. We show how analog experiments can be matched with numerical simulations for capturing the essential physics of the multiphase flow, obtaining calculated values of dynamic pressure in reasonable agreement with the experimental measurements. These outcomes encourage future application of the method for the assessment of the impact of pyroclastic density currents at the natural scale.     

A second-order curvilinear to Cartesian transformation of immersed interfaces and boundaries. Application to fictitious domains and multiphase flows

A global methodology dealing with fictitious domains of all kinds on curvilinear grids is presented. The main idea is to transform the curvilinear framework and its associated elements (velocity, immersed interfaces…) into a Cartesian grid. On such grids, many operations can be performed much faster than on curvilinear grids. The method is coupled with a Thread Ray-casting algorithm which works on Cartesian grids only. This algorithm computes quickly the Heaviside function related to the interior of an object on an Eulerian grid. The approach is also coupled with an immersed boundary method (L²-penalty) or with phase advection methods such as VOF–PLIC, VOF–TVD, Front-tracking or Level-set approaches. Applications, convergence and speed tests are performed for shape initializations, immersed boundary methods, and interface tracking.