Numerical simulation of pyroclastic density currents using locally refined Cartesian grids D.M. Doronzo a , M.D. de Tullio b , P. Dellino a , G. Pascazio b,⇑ a Centro Interdipartimentale di Ricerca sul Rischio Sismico e Vulcanico (CIRISIVU), c/o Dipartimento Geomineralogico, Università degli Studi di Bari, via Orabona 4, 70125 Bari, Italy b Dipartimento di Ingegneria Meccanica e Gestionale & Centro di Eccellenza in Meccanica Computazionale, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy article info Article history: Received 26 March 2010 Received in revised form 24 September 2010 Accepted 8 December 2010 Available online 16 December 2010 Keywords: Multiphase flow Cartesian grid Euler–Lagrange approach Column collapse Explosive volcanism abstract 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 ade- quate 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 vol- canic vent in order to reconstruct the steep velocity and particle concentration gradients. The grid gen- eration 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 essen- tial physics of the multiphase flow, obtaining calculated values of dynamic pressure in reasonable agree- ment 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. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Sediment density currents are geophysical surface flows that move over the Earth surface by means of the density difference between a multiphase fluid–particle mixture and the surrounding lean fluid [9]. The flow structure is subdivided into two parts [36]: the basal one moves as a shear current and develops a logarithmic velocity profile akin that of boundary layers, while the upper part has a velocity profile similar to the Gaussian one of free wall jets. The velocity maximum is reached on top of the shear flow, which is in between 1/3 and 1/4 of total flow thickness. The flow density, q mix (z)= q [1  C(z)] + q p C(z), where q and q p are the fluid and solid particle density respectively, decreases all the way throughout cur- rent height, z, according to the decrease of particle volumetric con- centration, C. The most noticeable examples of sediment density currents are the turbidity currents moving over the ocean floor and the pyroclastic density currents (PDCs) associated with explo- sive volcanic eruptions. Turbidity currents represent the main mean of sediment circulation in ocean basins, and the related deposits have a great importance since they are vast economic oil reservoirs [37]. PDCs, also known as pyroclastic flows, are initi- ated by the collapse of an eruption column (Fig. 1), which upon im- pact with the ground forms a shear current. The current thickens laterally and develops as a turbulent boundary layer shear flow [17]. These flows are hundreds of meters thick and move along the volcano slope and over the surrounding territory at speeds of tens of m/s and temperatures of hundreds of °C [6]. Their destructive power is demonstrated by historical events, the most famous example being the Pompeii eruption of Vesuvius [43,33]. For the aim of volcanic risk, flow dynamic pressure, P dyn (z) = 0.5 q mix (z)u 2 (z), where u is the flow velocity along the ground, is useful to territory planners to assess building resistance to the lat- eral stress exerted by the current [47,44]. Therefore, understanding the basic mechanism of column collapse is crucial to define models able to predict the hazard associated with PDCs. Our knowledge of the physics of PDCs comes from the geologi- cal record of the associated deposits (e.g., [4]), theoretical models (e.g., [5,17]) and numerical simulations (e.g., [48,22,38,12,23]). Modelling of column collapse and subsequent PDC evolution is ex- tremely challenging; in fact, the phenomenon involves the turbu- lent flow, of a rheologically complex fluid, in a wide range of scales (from 10 2 m at the ground to 10 m for the erupted column). Furthermore, since the current moves over the uneven topography surrounding the volcano, the ground surface is quite complex [31,46]. In particular, the multiphase numerical simulations per- formed until now demonstrate the unsteady nature and complex- 0045-7930/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compfluid.2010.12.006 ⇑ Corresponding author. E-mail address: pascazio@poliba.it (G. Pascazio). Computers & Fluids 44 (2011) 56–67 Contents lists available at ScienceDirect Computers & Fluids journal homepage: www.elsevier.com/locate/compfluid