Finite-Element Modeling in Engineering and Scientific Applications

Professor Carey and his group in the Computational Fluid Dynamics Laboratory develop and investigate new methods and algorithms to solve several classes of engineering and scientific problems. Their applications employ finite-element methods, in which the material domain of the problem is divided into numerous small volumes of identical or very similar geometry (e.g., tetrahedra). The physical properties of interest across the entire domain are then expressible as many sets of simultaneous equations, with each set derived from the boundary and interior conditions of a single finite element. The solution of these equations via matrix algebra over each time step supplies initial values for the following time steps, enabling the representation of changing conditions across the entire problem domain.

Currently, the group is working on flow problems for Newtonian and non-Newtonian fluids (the latter have changing viscosities), often coupled with heat and mass transfer. They are also interested in the phenomena of superconductivity and in flow and transport within complex fluids (like those containing solid particles or other inclusions, e.g., blood).

For a detailed description of one project completed in the Carey group, see the feature "Secrets of Shear Thinning."