Fluid–particle flow simulation by averaged continuous model Francesco Lalli a, * , Pier Giorgio Esposito b , Rodolfo Piscopia c , Roberto Verzicco d a Agenzia per la Protezione dell’Ambiente e per i Servizi Tecnici, via di Castel Romano 100, 00128 Roma, Italy b Telespazio SpA, via Tiburtina 965, 00156 Roma, Italy c Dipartimento di Idraulica, Trasporti e Strade, via Eudossiana 18, 00184 Roma, Italy d DIMeG and CEMeC, Politecnico di Bari, via Re David 200, 70125 Bari, Italy Received 16 December 2003; received in revised form 18 August 2004; accepted 30 August 2004 Available online 24 December 2004 Abstract In this paper we present a numerical method for fluid–particle flow simulation. The mathematical model is based on the averaged continuum. The presence of particles is taken into account in terms of effective viscosity, which is defined by means of both Newtonian and non-Newtonian (Bingham plastic) models. The dispersed phase equation closure is based on particle buoyancy as well as on shear-induced self-diffu- sion effects. The proposed approach allows us to study sediment transport problems and the related evolution of bed forms, without requiring the generation of curvilinear coordinate systems and time-con- suming step-by-step regridding. In fact, the present model describes the bottom shape in terms of a density contour surface, rather than a moving boundary of the fluid domain. Simple two-dimensional numerical tests have been performed: (i) Bingham flow in a driven cavity and (ii) particle settling in a pure Couette flow. Finally, preliminary results concerning (iii) two-dimensional scour below pipelines in steady flow have been presented and discussed. Ó 2004 Elsevier Ltd. All rights reserved. 0045-7930/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compfluid.2004.08.004 * Corresponding author. Tel.: +39 06 50073212; fax: +39 06 5050519. E-mail address: lalli@apat.it (F. Lalli). www.elsevier.com/locate/compfluid Computers & Fluids 34 (2005) 1040–1061