2D numerical simulation of density currents using the SPH projection method

Density currents (DCs) or gravity currents are driven by gravity in a fluid environment with density variation. Smoothed Particle Hydrodynamics (SPH) has been proved to have capabilities such as free surface modeling and accurate tracking of the immiscible-fluids interface that can be useful in the context of gravity currents. However, SPH applications to gravity currents have been limited to often-coarse simulations of high density-ratio currents. In this work, the SPH projection method is tried to solve currents with very low density-ratios (close to one), at a resolution, that captures the Kelvin-Helmholtz instabilities at the fluids interface. Existing implementations of the SPH projection method do not allow for an efficient solution of the currents with very low density-ratios. We found that a pressure-decoupling scheme inherently changes the way of distinguishing between the light and dense fluids in the projection method. Using this technique, SPH results, in a 2D lock-exchange flow at a Grashof number of 1.25×106 and Schmidt number of unity, are successfully compared with a previous grid-based simulation. Although these types of problems are well addressed in the past through grid-based methods, reproducing them with SPH reveals method's capabilities such as free surface modeling as advantages that can be benefited from in addressing relevant currents. DCs are often turbulent, but unfortunately, turbulence modeling is not yet well established in the SPH method. Nevertheless, there are opinions in the literature that SPH possesses some built-in mechanisms that compensate for the missing energy dissipation at the sub-particle scales. The results of our simulation and energy budget analysis of another lock-exchange flow at different levels of spatial resolution support this hypothesis, although do not provide conclusive evidence.