Numerical instabilities in bubble tracking in two-phase flow simulations

One way to model and simulate the dispersed phase in a two-phase flow is to track the discrete elements through a fluctuating fluid field by solving their equations of motion. It is shown that widely used and physically motivated discretization methods for the particle equation may lead to artificial instabilities yielding spurious oscillations and chaotic behavior via period-doubling bifurcations. This effect depends strongly on the form of the drag force exerted by the fluid on a discrete element, and is particularly pronounced in the case of bubbly flows.