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 summary

Program Title: PArallel Robust Interface Simulator — Paris

CPC Library link to program files: http://dx.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:

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Ftc3D: Front Tracking code for 3D simulations by Gretar Tryggvason and Sadegh Dabiri.

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Surfer: VOF code for 3D simulations by Stephane Zaleski, Jie Li, Ruben Scardovelli and others.

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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.

中文翻译：

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PArallel，坚固耐用，接口模拟器（PARIS）

巴黎（PArallel，鲁棒，接口模拟器）是用于模拟不混溶的多流体或多相流的有限体积代码。它基于Navier–Stokes方程的“单流体”公式，其中将不同的流体视为具有可变属性的一种材料，并将表面张力作为奇异的界面力添加。使用具有一阶或二阶时间积分方案的显式投影方法，在规则结构的交错网格上求解流体方程。通过Front-Tracking（FT）方法（通过连接的标记点表示该界面）或通过Volume-of-Fluid（VOF）方法（在其中将标记功能直接平移）来跟踪分离不同流体的界面。固定网格。巴黎用Fortran95 / 2002编写，并使用MPI和域分解进行并行化。它基于早期的FT或VOF代码，例如Ftc3D，Surfer或Gerris。这些代码和类似代码以及巴黎代码已用于模拟各种多流体和多相流。

计划摘要

程序名称： PArallel鲁棒接口仿真器—巴黎

CPC库链接到程序文件： http : //dx.doi.org/10.17632/5cb2yrfx7r.1

许可条款： GPLv3。

编程语言： Fortran95 / 2002。使用MPI和域分解并行化。

问题性质： 巴黎是一个免费代码或软件，用于多相流的计算流体动力学（CFD）（或计算多相流体动力学（CMFD）），专门用于界面流体流动的数值模拟，涉及液滴，气泡和波，如Tryggvason，Scardovelli和Zaleski [1]所述。它解决了两相流的单流体公式（包括表面张力）中的Euler或Navier-Stokes方程。它可以计算复杂的流量，例如快速雾化的射流或液滴，膨胀的空化气泡簇以及通过多孔介质的多相流量。

解决方法：该代码主要实现Tryggvason，Scardovelli和Zaleski [1]在书中描述的方法。时间步进是使用一阶或二阶时间预测器-校正器方法执行的，并带有显式的压力投影步骤。空间离散化是通过在规则长方体网格上的有限体积进行的。接口跟踪是使用前跟踪（FT）方法或流体体积（VOF）方法执行的。在VOF版本的巴黎使用拉格朗日显式（LE）对流方法或Weymouth and Yue [2]的精确质量守恒方法。正常计算使用混合杨氏中心（MYC）方案执行。质量-动量对流方法也已经实现，与VOF对流一致[3]。曲率通过高度函数（HF）方法计算。结合平衡连续表面力（CSF）方法计算表面张力。

如果可以忽略一个阶段的动力学，巴黎也可以通过指定一个被忽略的阶段中最大随时间变化的均匀压力来作为自由表面代码运行。在雾化喷嘴的情况下，巴黎已经实施了一种算法，该算法可以检测孤立的液滴，将其平整为拉格朗日点粒子，并可能再次与主流合并

附加说明： 巴黎源自以下代码或受其启发：

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Ftc3D：Gretar Tryggvason和Sadegh Dabiri进行3D模拟的前端跟踪代码。

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冲浪者：Stephane Zaleski，Jie Li，Ruben Scardovelli等人的3D模拟的VOF代码。

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Gerris：Stephane Popinet的具有自适应网格细化（AMR）的多相流求解器。

参考

[1] G. Tryggvason，R。Scardovelli和S. Zaleski。气液多相流的直接数值模拟。剑桥大学出版社，2011年。

[2] G. D. Weymouth和Dick K. P. Yue。笛卡尔网格上自由表面模拟的保守流体体积方法。计算物理杂志，229（8）：2853-2865，2010年4月。

[3] T. Arrufat，M。Crialesi-Esposito，D。Fuster，Y。Ling，L。Malan，S。Pal，R。Scardovelli，G。Tryggvason，S。Zaleski，质量动量一致，体积-用于交错网格上不可压缩流的流体方法，计算机与流体，215，104785，2021。