Abstract
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.
Program Title: PArallel Robust Interface Simulator — Paris
CPC Library link to program files:https://doi.org/10.17632/5cb2yrfx7r.1
Licensing provisions: GPLv3.
Programming language: Fortran95/2002. Parallelized using MPI and domain decomposition.
Nature of problem:Paris is a free code, or software, for computational fluid dynamics (CFD) of multiphase flows (or computational multiphase fluid dynamics (CMFD)), specialized in the numerical simulation of interfacial fluid flows, involving droplets, bubbles and waves, as described in the book by Tryggvason, Scardovelli and Zaleski [1]. It solves the Euler or Navier–Stokes equations in the one-fluid formulation of two-phase flow, including a surface tension force. It computes complex flows such as fast atomizing jets or droplets, expanding cavitation bubble clusters and multiphase flow through porous media.
Solution method: The code mostly implements the methods described in the book by Tryggvason, Scardovelli and Zaleski [1]. Time stepping is performed using a first-order or a second-order in time predictor–corrector method with an explicit projection step for the pressure. Spatial discretization is by finite volumes on a regular cuboid grid. Interface tracking is performed with the Front-Tracking (FT) method or the Volume-of-Fluid (VOF) method. In the VOF version Paris uses either the Lagrangian-Explicit (LE) advection method or the exactly mass-conserving method of Weymouth and Yue [2]. The normal computation is performed using the Mixed-Youngs-Centered (MYC) scheme. A mass–momentum advection method has been also implemented that is consistent with the VOF advection [3]. Curvature is computed with the Height Function (HF) method. This is combined with the balanced Continuous Surface Force (CSF) method to compute surface tension forces.
If the dynamics of a phase can be neglected, Paris can also run as a free-surface code by specifying a homogeneous pressure, at most varying with time, in the neglected phase. In the case of atomizing jets, an algorithm has been implemented in Paris that can detect isolated droplets, advects them as Lagrangian point-particles and possibly merge them again with the main stream
Additional comments:Paris is extended from or inspired by the following codes: •Ftc3D: Front Tracking code for 3D simulations by Gretar Tryggvason and Sadegh Dabiri.•Surfer: VOF code for 3D simulations by Stephane Zaleski, Jie Li, Ruben Scardovelli and others.•Gerris: multiphase flow solver with Adaptive Mesh Refinement (AMR) by Stephane Popinet.
References
[1] G. Tryggvason, R. Scardovelli, and S. Zaleski. Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press, 2011.
[2] G. D. Weymouth and Dick K. P. Yue. Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids. Journal of Computational Physics, 229(8):2853–2865, April 2010.
[3] T. Arrufat, M. Crialesi-Esposito, D. Fuster, Y. Ling, L. Malan, S. Pal, R. Scardovelli, G. Tryggvason, S. Zaleski, A mass–momentum consistent, Volume-of-Fluid method for incompressible flow on staggered grids, Computers & Fluids, 215, 104785, 2021.