Buoyancy modelling with incompressible SPH for laminar and turbulent flows

This 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.