triflow 0.4.0

Python library for falling-films modeling

Installation

External requirements

The library is based on Theano, thus extra dependecies like fortran and C compiler are needed, see Theano install page for extra informations:

http://deeplearning.net/software/theano/install.html

via PyPI

Beware, the PyPI version is not always up-to-date.

pip install triflow

will install the package and

pip install triflow --upgrade

will update an old version of the library.

use sudo if needed, and the user flag if you want to install it without the root privileges:

pip install --user triflow

via github

You can install the last version of the library using pip and the github repository:

pip install git+git://github.com/locie/triflow.git

Introduction

Motivation

The aim of this library is to have a (relatively) easy way to write transient dynamic systems with 1D finite difference discretisation, with fast temporal solvers.

The main two parts of the library are: * symbolic tools defining the spatial discretisation, with boundary taking into account in a separated part * a fast temporal solver written in order to use the sparsity of the finite difference method to reduce the memory and CPU usage during the solving

Moreover, extra tools are provided and the library is written in a modular way, allowing an easy extension of these different parts (see the plug-in module of the library.)

The library fits well with an interactive usage (in a jupyter notebook). The dependency list is actually larger, but on-going work target a reduction of the stack complexity.

Model writing

All the models are written as function generating the F vector and the Jacobian matrix of the model defined as

\begin{equation*} \frac{\partial U}{\partial t} = F(U) \end{equation*}

The symbolic model is written as a simple mathematic equation. For exemple, a diffusion advection model can be written as:

from triflow import Model

func = "k * dxxU - c * dxU"
var = "U"
pars = ["k", "c"]

model = Model(func, var, pars)

Example

import numpy as np
from triflow import Model, Simulation
from triflow.plugins.displays import bokeh_probes_update


model = Model(funcs="k * dxxU - c * dxU", vars="U", pars=["k", "c"])
parameters = dict(time_stepping=True,
                  tol=1E-1, dt=1, tmax=100,
                  periodic=True,
                  c=1, k=1E-6)

x = np.linspace(-2 * np.pi, 2 * np.pi, 100, endpoint=False)
U = np.cos(x) + 2

fields = model.fields_template(x=x, U=U)
simul = Simulation(model, fields, 0, parameters)

def internal_iter(t, simul):
    return simul.scheme.internal_iter

bokeh_probe = bokeh_probes_update({'niter': internal_iter})

for fields, t in simul:
    bokeh_probe.send((t, simul))