Benchmarking rigid bodies moving in fluids using Feel++ Supplementary Material

Authors

• Luca Berti

• Vincent Chabannes

• Laetitia Giraldi

• Christophe Prud’homme

The directories contain the supplementary material to reproduce the results of the paper "Benchmarking rigid bodies moving in fluids using Feel++", see https://hal.science/hal-03835136

The benchmarks can be run from a Linux Ubuntu 20.04(focal) or 22.04(jammy) system or with a docker container.

We used Feel++ v110 which can be cited as follows

Christophe Prud'homme, Vincent Chabannes, Thibaut Metivet, Romain Hild, Trophime, Abdoulaye SAMAKE, Thomas Saigre, Philippe Ricka, & Luca Berti. (2021). feelpp/feelpp: Feel++ V109 (v0.109.0). Zenodo. https://doi.org/10.5281/zenodo.5718297

The development version v110 can be used as well.

Feel++ Installation

Install Feel++ in Ubuntu 20.04 or 22.04

The installation procedure of Feel++ is described here.

Install Dockler if needed

See https://docs.docker.com/engine/install/ for the procedure

Pull the docker container

Pull the docker image

docker pull ghcr.io/feelpp/feelpp:focal

Run the benchmarks

First clone the article complementary material

Clone complementary material

$ git clone https://github.com/feelpp/article.fluid_rigid_body_ale
$ cd article.fluid_rigid_body_ale

If you want to use docker, run the following that will mount the current directory of the top level folder of the article

$ docker run --rm -it -v $PWD:/mnt ghcr.io/feelpp/feelpp:focal

You then have a prompt from docker ubuntu focal

feelpp@dda2cfdd6120:/$ ls /mnt
README.adoc  cylinder_2d  ellipsoid_2d  ellipsoid_3d  fluid.py  sphere
feelpp@dda2cfdd6120:/$  cd /mnt

To run the benchmarks using 4 mpi processes

Falling sphere in a Stokes flow

mpirun -np 4 feelpp_toolbox_fluid --case sphere

Falling 3D prolate ellipsoid in a Stokes flow

mpirun -np 4 feelpp_toolbox_fluid --config-files ellipsoid_3d/dev/C1.cfg ellipsoid_3d/dev/pcd.cfg

Falling 2d ellipsoid in a Laminar flow

mpirun -np 4 feelpp_toolbox_fluid --case ellipsoid_2d

Falling 2d cylinder in a Laminar flow

mpirun -np 4 feelpp_toolbox_fluid --case cylinder_2d

Reproduction of paper results

All information of a simulation are stored in a directory whose path is given at the end of the execution. Considering the terminal at the end of the simulation of the cylinder:

+---------------------------------------------------------------------------------------+
|                                   application_fluid                                   |
+---------------------------------------------------------------------------------------+
| +-------------+---------------------------------------------------------------------+ |
| | logs        | /home/feelpp/feelppdb/toolboxes/fluid/cylinder_2d/np_4/logs         | |
| +-------------+---------------------------------------------------------------------+ |
| | journal     | /home/feelpp/feelppdb/toolboxes/fluid/cylinder_2d/np_4/journal.json | |
| +-------------+---------------------------------------------------------------------+ |
| | directories | +--------------------------------------------------------+          | |
| |             | | /home/feelpp/feelppdb/toolboxes/fluid/cylinder_2d/np_4 |          | |
| |             | +--------------------------------------------------------+          | |
| |             | | /mnt                                                   |          | |
| |             | +--------------------------------------------------------+          | |
| +-------------+---------------------------------------------------------------------+ |
+---------------------------------------------------------------------------------------+

one can notice that the path of the directory is given by: /home/feelpp/feelppdb/toolboxes/fluid/cylinder_2d/np_4.

The files used to reproduce the paper results are the folder labeled "fluid.exports" allowing to visualize the simulation using Paraview, and the "values.csv" file in the "fluid.measures" folder storing the results of the simulation in form of columns, i.e. each column stores the values of one quantity for each time instant.

To read and store the quantities of the csv files, one uses the library Pandas of Python:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# Read and store csv
data = pd.read_csv("values.csv") #Read csv file
data.columns = data.columns.str.strip()

xcm = np.array(data["Quantities_body_p1_mark.mass_center_0"])
ycm = np.array(data["Quantities_body_p1_mark.mass_center_1"])
rot = np.array(data["Quantities_body_p1_mark.rigid_rotation_angle"])
time = np.array(data["time"])

The last four lines store the quantities of interest using the column name. For the graphs shown in the paper, one requires the following quantities:

• mass_center_0: x-coordinate of the center of mass

• mass_center_1: y-coordinate of the center of mass in 2d and z-coordinate in 3d

• rigid_rotation_angle: rotation angle

• time: time instant

The name of each column is defined by the name of the quantity, followed by the name given to the body. For the previous example, the name given to the body is Quantities_body_p1_mark.

Finally, one can plot the quantities. The following code allows plotting the graphs by defining x, y and the labels:

# Plot results
figure, axis = plt.subplots(figsize=(15,10))
axis.plot(time,ycm,label="Paper results") # Plot y=ycm versus x=time
axis.set_xlabel("Time") # Define x label
axis.set_ylabel("ycm") # Define y label
axis.legend(loc='best')

This example shows the evolution of the y-coordinate of the cylinder center of mass versus time.