Dual-Lattice Modeling of Transport in Heterogeneous Materials
John E. Bolander, T. Saka, MM Rashid · 2015
Coupled elasticity and potential flow problems, such as drying shrinkage, can be solved using lattice models. Typically, both the displacement and relative humidity fields are represented by the same set of nodes. When considering crack development and its influences on transport, however, it may be advantageous to use a different lattice for each field. In this research, the structural problem is to be solved using a lattice defined by the edges of the Delaunay tessellation of a set of nodal points. The edges of the dual Voronoi diagram are used to solve the flow problem. In this way, flow elements are better positioned to simulate transport along cracks, the effects of crack opening on such flow, and transport from the crack faces into the bulk material. A complicating factor is the inevitable occurrence of arbitrarily small and/or poorly-shaped geometric objects associated with the Voronoi diagram. These features can both degrade the physical fidelity of the simulation results, and negatively impact the reliability of the overall simulation process. This research introduces the concept of automated tolerance-driven domain discretization, by which undesirable features of the Voronoi diagram are avoided at the mesh-generation stage. Corresponding improvements in the ability to reliably model flow in homogeneous and heterogeneous solids are demonstrated. Potential improvements in the modeling of fracture and flow through fractured media are discussed.