Chair of Physics & Professor Philip Yecko Co-Authors Paper in the Journal of Computer Physics Communication

POSTED ON: July 7, 2021


The Cooper Union is home to a new and free open-source CFD code for direct numerical simulations of multi-phase and multi-fluid flows described by Navier-Stokes equations. Physics Departmental Chair, Professor Philip Yecko, is part of an international team that developed the Parallel, Robust, Interface Simulator (PARIS) code beginning in 2015.  

The goal of PARIS is to make possible new fundamental research simulations of bubbles, droplets and sprays, flow in porous media, and other complex flows by easily incorporating new physics and by being efficient - often at speeds 100 times or more faster than commercial codes like ANSYS.  

Professor Yecko, with his students and collaborators, also extended PARIS to model bulk and interfacial magnetic fields and stresses, using the code on High Performance Computing supercomputers to study magnetic drug delivery. 

The code was recently published, both as a paper and as software, in the June 2021 issue of the journal Computer Physics Communications. The paper can be read here:


Paris (Parallel, Robust, Interface Simulator) is a finite volume code for simulations of immiscible multifluid or multiphase flows. It is based on the “one-fluid” formulation of the Navier–Stokes equations where different fluids are treated as one material with variable properties, and surface tension is added as a singular interface force. The fluid equations are solved on a regular structured staggered grid using an explicit projection method with a first-order or second-order time integration scheme. The interface separating the different fluids is tracked by a Front-Tracking (FT) method, where the interface is represented by connected marker points, or by a Volume-of-Fluid (VOF) method, where the marker function is advected directly on the fixed grid. Paris is written in Fortran95/2002 and parallelized using MPI and domain decomposition. It is based on several earlier FT or VOF codes such as Ftc3D, Surfer or Gerris. These codes and similar ones, as well as Paris, have been used to simulate a wide range of multifluid and multiphase flows.

  • Founded by inventor, industrialist and philanthropist Peter Cooper in 1859, The Cooper Union for the Advancement of Science and Art offers education in art, architecture and engineering, as well as courses in the humanities and social sciences.

  • “My feelings, my desires, my hopes, embrace humanity throughout the world,” Peter Cooper proclaimed in a speech in 1853. He looked forward to a time when, “knowledge shall cover the earth as waters cover the great deep.”

  • From its beginnings, Cooper Union was a unique institution, dedicated to founder Peter Cooper's proposition that education is the key not only to personal prosperity but to civic virtue and harmony.

  • Peter Cooper wanted his graduates to acquire the technical mastery and entrepreneurial skills, enrich their intellects and spark their creativity, and develop a sense of social justice that would translate into action.