Buoyancy modelling with incompressible SPH for laminar and turbulent flows

• Published in: International journal for numerical methods in fluids Vol. 78; no. 8; pp. 455 - 474
• Main Authors: Leroy, A., Violeau, D., Ferrand, M., Joly, A.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 20.07.2015; Wiley Subscription Services, Inc; Wiley
• Subjects: boundary conditions; Buoyancy; Computational fluid dynamics; Engineering Sciences; Fluid flow; Fluids mechanics; incompressible; Laminar; Mathematical models; Mechanics; SPH; temperature; Turbulence; Turbulent flow; Walls; SPH; incompressible; turbulence; boundary conditions; buoyancy
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4025

SummaryThis work aims to model buoyant, laminar or turbulent flows, using a two‐dimensional incompressible smoothed particle hydrodynamics model with accurate wall boundary conditions. The buoyancy effects are modelled through the Boussinesq approximation coupled to a heat equation, which makes it possible to apply an incompressible algorithm to compute the pressure field from a Poisson equation. Based on our previous work [1], we extend the unified semi‐analytical wall boundary conditions to the present model. The latter is also combined to a Reynolds‐averaged Navier–Stokes approach to treat turbulent flows. The k − ϵ turbulence model is used, where buoyancy is modelled through an additional term in the k − ϵ equations like in mesh‐based methods. We propose a unified framework to prescribe isothermal (Dirichlet) or to impose heat flux (Neumann) wall boundary conditions in incompressible smoothed particle hydrodynamics. To illustrate this, a theoretical case is presented (laminar heated Poiseuille flow), where excellent agreement with the theoretical solution is obtained. Several benchmark cases are then proposed: a lock‐exchange flow, two laminar and one turbulent flow in differentially heated cavities, and finally a turbulent heated Poiseuille flow. Comparisons are provided with a finite volume approach using an open‐source industrial code. Copyright © 2015 John Wiley & Sons, Ltd. This work aims to model buoyant, laminar or turbulent flows, using a two‐dimensional incompressible smoothed particle hydrodynamics model with accurate wall boundary conditions. Thek − ϵ turbulence model is used, where buoyancy is modelled through an additional term in the k − ϵ equations. Several benchmark cases are then proposed including heated Poiseuille flows, differentially heated cavities and a lock‐exchange flow. Good agreement is obtained with a finite volume approach using an open‐source industrial code.