ISPH modelling of transient natural convection

Abstract

Transient and laminar natural convection in a square cavity has been investigated using smoothed particle hydrodynamics (SPH) technique as a discretisation tool on uniform Eulerian grids. Although SPH is a mesh-free Lagrangian method and always applied to discretise Lagrangian form of governing equations, in this study, Eulerian form of governing equations are discretised using SPH operators. This approach is thought to be the upper limit of accuracy of Lagrangian SPH computations by preventing density error accumulation and particle disordering. In the present method, incompressibility is strictly enforced by employing SPH pressure projection method in order to obtain a divergence-free velocity field as in incompressible SPH (ISPH) method. Natural convection in a square cavity is simulated for Rayleigh numbers, Ra, between 103 and 106. Effect of Ra on the flow field and heat transfer characteristics is investigated and the method is validated by data available in the literature. Results obtained from ISPH method on Eulerian grids are in excellent agreement with data available in the literature. © 2013 Copyright Taylor and Francis Group, LLC.