Modeling of natural convection with Smoothed Particle Hydrodynamics: Non-Boussinesq formulation

A new variant of the Smoothed Particle Hydrodynamics (SPH) simulations of the natural convection phenomena is introduced. In many situations, where the density may vary significantly under the influence of temperature non-uniformities, the classical Boussinesq approximation fails. To characterize such situations, the Gay-Lussac dimensionless number is useful as a measure of density variations in non-isothermal flows. The novel points of the proposed modeling beyond the Boussinesq regime include the proper implementation of the buoyancy force and a smart connection between particle volume and incompressibility constraint. To examine the correctness of the new approach, numerical results are confronted with available reference data.