Detail of the project MOOSE

1. Presentation

MOOSE, Multiphysics Object-Oriented Simulation Environment, is an open-source, parallel finite element framework.

There are many application in MOOSE, but the most interresting for us is HeatConduction (www.mooseframework.org/modules/heat_conduction/index.html)

The part of radiative heat transfer is develop in these book, see Monte Carlo method.

2. Most important

The part most important for stage is the calculation of view factor.

The source code of calculation of view factor is in github.com/idaholab/moose/tree/next/modules/heat_conduction/src/userobjects. And class are in : github.com/idaholab/moose/tree/next/modules/heat_conduction/include/userobjects

The code source contains :

  • ViewFactorBase.h and ViewFactorBase.C : contains the class ViewFactorBase which represents view factors between chosen boundaries (surface).

  • UnobstructedPlanarViewFactor.h and UnobstructedPlanarViewFactor.C : contains the class UnobstructedPlanarViewFactor inherited from ViewFactorBase and represents view factors between the surfaces of an enclodure with no obstruction between surfaces (we must have \(\sum_{j=1}^I{F_{A_i \rightarrow A_j}}\)). The method execute computes the view factors with a method of quadrature.

3. Method of quadrature of Gauss

3.1. Theory general

The method of quadrature is detail in classes. The goal is to approximate a integral in discrete sum.

Set \(K\) finite surface in \(\mathbb{R}^2\), the integrable function \(\phi : K \rightarrow \mathbb{R}\). We introduce some points \(\{\xi_i\}_{i \leq N}\) in \(K\) with associated weight \(\{\omega_i\}_{i \leq N}\). We have the approximation :

\[\int_{K}{\phi d\lambda} = \sum_{i=1}^N{ \omega_i \phi(\xi_i)}\]

References