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Journal of Computational Physics 201 (2004) 397–420 www.elsevier.com/locate/jcp On a numerical strategy to compute gravity currents of non-Newtonian fluids
D. Vola *, F. Babik, J.-C. Latch e Direction de la Prvention des Accidents Majeurs, Institut de Radioprotection et de S^ret Nuclaire (IRSN), e u e e BP3-13115 St. Paul-lez-Durance Cedex, France
Received 20 October 2003; received in revised form 15 March 2004; accepted 28 May 2004
Available online 6 July 2004

Abstract
This paper is devoted to the presentation of a numerical scheme for the simulation of gravity currents of nonNewtonian fluids. The two dimensional computational grid is fixed and the free-surface is described as a polygonal interface independent from the grid and advanced in time by a Lagrangian technique. Navier–Stokes equations are semi-discretized in time by the Characteristic-Galerkin method, which finally leads to solve a generalized Stokes problem posed on a physical domain limited by the free surface to only a part of the computational grid. To this purpose, we implement a Galerkin technique with a particular approximation space, defined as the restriction to the fluid domain of functions of a finite element space. The decomposition–coordination method allows to deal without any regularization with a variety of non-linear and possibly non-differentiable constitutive laws. Beside more analytical tests, we revisit with this numerical method some simulations of gravity currents of the literature, up to now investigated within the simplified thin-flow approximation framework.
Ó 2004 Elsevier Inc. All rights reserved.
Keywords: Free surface flows; Viscoplastic fluids; Herschel–Bulkley model; Fictitious node FEM; Characteristics/Galerkin method;
Decomposition–coordination method; Gravity currents

1. Introduction
Free-surface flows are involved in a wide range of phenomena, including both natural hazards (mud or lava flows for instance) and industrial applications (mould

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