Published: March 12, 2021

Marsha Berger; Silver Professor of Computer Science and Mathematics; Courant Institute of Mathematical Sciences, New York University

Computing Fluid Flows in Complex Geometry

We give an overview of the difficulties in simulating fluid flow in complex geometry.  The principal approaches use either overlapping or patched body-fitted grdis, unstructured grids, or Cartesian (non-body-fitted) grids, with our work focusing on the latter.  Cartesian methods have the advantage that no explicit mesh generation is needed, greatly reducing the human  effort involved in complex flow computations.  However it is a challenge to find stable and accurate difference formulas for the irregular Cartesian cells cut by the boundary.

We discuss some of the steps involved in preparing for and carrying out a fluid flow simulation in complicated geometry. We present some of the technical issues involved in this approach,  including the special discretizations needed to avoid loss of accuracy and stability at the irregular cells, as  well as how we obtain highly scalable parallel performance. This method is in routine use for aerodynamic calculations in several organizations, including NASA Ames Research Center. Several open problems are discussed.

Bio: Marsha Berger is Silver Professor of Computer Science and Mathematics in the Courant Institute of Mathematical Sciences of New York University.  Her work specializes in the development of numerical methods for large scale fluid dynamic simulations which must be run in a parallel computing environment.  Much of her (recent) work has been dedicated to the accurate simulation of tsunamis caused by many factors including earthquake, landslide and asteroid.  The numerical tools that she develops are utilized in engineering design to prevent flooding as well in the plan for escape routes in case of an emergency.  Dr. Berger is a member of the National Academy of Sciences, National Academy of Engineering, a SIAM fellow and the recipient of too many awards to cite. Recently, Dr. Berger became a group leader in the Center for Computational Mathematics at the Flatiron Institute.