A Discrete Differential Geometric Approach for Simulation of Coupled Multiphase Mesoporous Systems

A myriad of processes and systems in Chemical- and other fields of Engineering Science are multiphase. Applications that involve processes containing multiple phases of increasing geometric complexity have become increasingly common in recent years. Attempts to model and simulate systems with a large number of interfaces with complex geometries is often limited by the interface tracking and accuracy of the curvature computation which is a large source of error of the numerical method. This work resolves the long standing difficulty in computing the curvature of interfaces accurately and efficiently.

In this work a new practical tool was developed that can be implemented in a wide array of state-of-the art methods. It is shown that the rigorous derivation of the curvature of interfaces allows for an accurate, or near-exact computation of curvature for simulation of three-phase systems. Additionally, it is demonstrated that a special trapezoidal integration error can be used to provide an estimate of continuity of the interface, which is useful for ensuring dynamic accuracy in three-phase simulations by controlling the refinement of a numerically captured fluid-fluid interface that is manifold.

It is further shown that the method for computing curvatures developed herein can be computed exactly for arbitrary fluid-fluid interfaces that are manifold. The extent to which an interface is manifold can be tracked by computing the topology of the simplicial complex using computationally efficient methods developed especially for this application. Since the method for computing curvatures are near-exact and mesh independent, a very large tolerance can be used in large scale simulation of complex three-phase materials. In principle, it is only necessary to track that the interface is continuous. Therefore, the complex can be refined in such a way that the error matches the desired tracking of non-solid volume due to porosity and asperities in three-phase systems. The result of this work can be implemented in any formulation where the underlying geometry of the model is manifold, and is especially useful in the fields of multiphase flow, thermodynamics, materials engineering and surface energy minimisation.