Development of a grid-supported marker particle scheme for interface tracking

A methodology is presented to simulate the growth and interaction of unstable fronts. Such fronts are found to be important in instabilities arising in several natural and industrial processes, such as solidification, spray dynamics, and bubble growth. The numerical simulation of such phenomena is challenging on account of the highly distorted moving boundary at which, often, curvature-dependent boundary conditions need be applied in each phase. Herein is presented a numerical technique to capture highly distorted interfaces. The interface is represented employing marker particles. Joining successive markers with circular arcs yields values of curvatures and normals on the interface. The markers are followed over an underlying cartesian grid and new marker particles are generated at each time step by an intersection procedure. The issue of mergers of interfaces is also attacked and the use of cells permits the simulation of merger-breakup processes. Thus, the method presented here, unlike previous marker particle based schemes, can handle particle depletion/accumulation and mergerbreakup issues with good accuracy. Results are presented, employing velocity functions modeled to mimic the actual instability phenomena, to demonstrate the accuracy and capability of the scheme developed.