Node to node contacts for SPH applied to multiple fluids with large density ratio

The interesting and complex behavior of fluids emerges mainly from interaction processes. SPH has shown to be a simple, yet flexible method to cope with many fluid simulation problems in a robust way. However in SPH, particles have a spatial distance (smoothing length) over which their properties are smoothed by a kernel function. Smoothed quantities of a particles show falsified values when densities and masses of neighboring particles vary largely within the smoothing length. The erroneous quantities lead to undesirable effects, reaching from unphysical density and pressure variations to spurious and unnatural interface tensions, and even to severe numerical instabilities. In this paper, instead of using the traditional interaction between SPH parts through SPH interpolation, we present a node to node contact between different SPH parts to avoid the instabilities due to large density ratios at the interfaces. The methods allow the users to select the desired amount of contact force between two SPH parts by choosing the desired penalty scale factors according to the simulation problem at hand. Some examples are tested to show that the method was successfully used to stably simulate multiple fluids with large density contrasts without the above described artifacts apparent in standard SPH simulation.