Disclaimer : under construction

Tags :

• open_source : pypi, gitlab.com, readthedocs.
• CFD : 2 CFD solvers, one Navier-Stokes, one Lattice Boltzmann.
• training : dedicated to CFD training.
• Python package : available on pypi.

# Barbatruc - Finite Differences Navier-Stokes and LBM for CFD training.

Barbatruc is a package for Computational Fluid Dynamics (CFD) trainings. This repository is education-oriented and illustrates the principle of dependency inversion for CFD-solvers. It becamed a side product of the EXCELLERAT Center of Excellence project, funded by the EU.

There are three basic cases developed in barbatruc: a poiseuille 2D flow, a lid-driven cavity flow and a flow around a cylinder. Each one of these examples has a simplified data-structure for a cartesian, regular i-j mesh. The solvers must fit into this datastructure, without interferring.

For each case, a time loop is used to solve it, the setup is as follow:

Finite differences forward explicit solver for Navier-Stokes

```solver = NS_fd_2D_explicit(dom, max_vel=2*vel)
for i in range(nsave):
time += time_step
solver.iteration(time, time_step)
print("\n\n===============================")
print(f"\n  Iteration {i+1}, Time :, {time}s")
print(f"  Reynolds : {dom.reynolds(width)}")
print(dom.fields_stats())
dom.dump_paraview(time=time)
```

By the end of 2019, two solvers are implemented with the same signature :

• Explicit finite difference solver, rewritten from Lorena Barba, in 200 lines.

• Lattice Boltzmann 2DQ9 solver, in 400 lines.

Be aware that the Lattice Boltzmann solver (LBM) is not ready for release yet.

## Poiseuille

This is the simplest case you can find in barbatruc.

There are two cases for Poiseuille.

### First case:

It consists of periodic boundary conditions as input and output, and no slip conditions as lower and upper wall with Re = 100.

Because there is no input velocity, a volumic force (or source term) is added for the flow to develop, it simulates the pressure gradient.

For further information go to the periodic Poiseuille flow documentation

Script for Poiseuille periodic flow:

```    """Example on how to solve a Poiseuille problem  with the navier stokes solver"""

import numpy as np
import matplotlib.pyplot as plt
from barbatruc.fluid_domain import DomainRectFluid
from barbatruc.fd_ns_2d import NS_fd_2D_explicit
#from barbatruc.lattice import Lattice

__all__ = ["cfd_poiseuille"]

# pylint: disable=duplicate-code
def cfd_poiseuille(nsave):
"""Startup computation
solve a poiseuille problem
"""

width = 1.
length = width*4
dimx=length
vel = 1.0
t_end = 10.*length/vel
nu_ = 0.01
ncell = 15
d_x = width/ncell
dimy=width+d_x
delta_x=width/ncell
rho=1.12
dom = DomainRectFluid(
dimx=dimx,
dimy=dimy,
delta_x=delta_x,
nu_=nu_,
rho=rho)

dom.switch_bc_ymax_wall_noslip()
dom.switch_bc_ymin_wall_noslip()
dom.fields["vel_u"] += vel
dom.set_source_terms({
"force_x": 8. * nu_ / width**2. * np.ones(dom.shape) * vel,
"force_y": np.zeros(dom.shape),
"scal": np.zeros(dom.shape)
})

print(dom)

time = 0.0
time_step = t_end/nsave

#solver = Lattice(dom, max_vel=3*vel)
solver = NS_fd_2D_explicit(dom, max_vel=1.8)
for i in range(nsave):
time += time_step
solver.iteration(time, time_step)
print("\n\n===============================")
print(f"\n  Iteration {i+1}/{nsave}, Time :, {time}s")
print(f"  Reynolds : {dom.reynolds(width)}")
print(dom.fields_stats())
dom.dump_paraview(time=time)
dom.dump_global(time=time)

y = np.linspace(0,1.07,num=1000)
u=np.zeros(len(y))
u_bulk=0.66
Umax=(3/2)*u_bulk

for i in range(len(y)):
u[i]=Umax*4*(y[i]/dimy)*(1-(y[i]/dimy))
plt.plot(y,u,color="red",marker="", label= 'theoretical curve')

dom.show_profile_y()
solver.plot_monitor()
dom.show_fields()
dom.show_flow()
dom.show_debit_over_x()

print('Normal end of execution.')

if __name__ == "__main__":
cfd_poiseuille(10)
```

### Second case:

This a Poiseuille flow with an input velocity and Re = 300

It must give the following image. But be aware that the jupyter notebook is under construction and might not display the images because of a version upgrade.

## Cavity

A lid-driven cavity simulation at Re = 300 will look like:

For further information go to the cavity documentation

## Cylinder

The goal is to simulate Von-Karman street with a vortex-shedding frequency.

At Re = 100, we have a cylinder in cross flow:

For further information go to the cylinder documentation

Lucille Laberie was a Master 1 internship student at Cerfacs during summer 2020.