Discrete Exterior Calculus and Its Application to CFD


In most engineering applications of fluid and solid mechanics, the need of working with simple models formulated in Euclidean spaces has resulted in overlooking geometric methods and hence a disconnect between different theories/models/methods and a lack of a deep understanding of the connections between different numerical methods, structure of governing equations of discrete and continuous systems. Therefore, we are interested in exploring ideas and techniques from differential geometry, exterior calculus, and algebraic topology and their potential to provide the basis for an alternative/efficient paradigm to solve the governing equations of various fluid and solid mechanics applications.


Georgia Institute of Technology, University of Oxford