Buoyancy-driven circulation and multi-component mixing using SPH with a new adiabatic boundary condition

Multi-component fluid mixing by buoyancy-driven circulation is a common engineering process. Buoyancy-driven flows have been studied extensively using mesh-based Eulerian methods, but challenges remain especially near the fluid component interface. Smoothed particle hydrodynamics (SPH) is a meshless Lagrangian method able to deal with large deformations and a changing interface between the fluid components. Herein, an SPH formulation is proposed by employing the Boussinesq approximation to model buoyancy-driven flows where the temperature evolves by a governing equation, as well as multiple components with variable viscosities. In addition, a new implementation of an adiabatic boundary condition in SPH is included by adapting the recently developed modified dynamic boundary condition. The SPH results are compared against reference solutions for 2-D and 3-D, single and multi-component cases such as a differentially heated cavity and a cylindrical tank. Agreement is found with reference solutions for differentially heated cavity cases, provided the ratio of smoothing length to particle size is sufficiently large. Furthermore, the combined volume fraction - finite time Lyapunov exponent mixing measure gives insight into the relative movement of components at both a local and global level.