N-Phase Interface Tracking Method Based on Prime Enumeration of Microcells

This paper presents a general method for tracking N incompressible materials and their associated interfaces, where N may be an integer greater than 2. Two key components are fundamental to the method. First, is the concept of a microgrid element or cell, which is uniquely identified or associated with a fluid material. Second, is a method for uniquely identifying a microcell through the use of prime numbers. The approach implements a microcell methodology embedded on a regular grid to further subdivide and then tag the material components of the computational system via a prime numbering algorithm. The microcells motion are then tracked, driven by local velocity conditions computed at the macrogrid level, and rectifying small anomalies by a coupled evaluation of local volume fraction fields and global mass conservation. Volume fractions can be calculated at any time step by an evaluation of the prime number distribution so that average cellular density and viscosity values can be regularly updated at the macrogrid level. This paper, then, presents the details of the microgrid method and illustrates its capabilities through two-dimensional, N-component, problem simulations.