O. Pironneau | On the radiative transfer equations

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Olivier Pironneau (Sorbonne Universit´e)
On the radiative transfer equations

In continuum mechanics radiative transfer is modelled by an integro- differential system of equations with a time variable, 3 space variables and two angular variables. It is numerically very challenging, especially that applications to climate and combustion require frequency dependent coefficients and coupling with the Navier-Stokes equations. Nevertheless, by using a formulation due to Chandrasekhar, existence and uniqueness can be established as a limit of an increasing sequence with very few constraints on the coefficients. The same property leads to a fast numerical algorithm with a ray-tracing type step and a convolution step accelerated by the H-matrix algorithm. Numerical results will be shown for the earth atmosphere and for the effect of sunlight on Boussinesq’s instabilities in a lake.In continuum mechanics radiative transfer is modelled by an integro-differential system of equations with a time variable, 3 space variables and two angular variables. It is numerically very challenging, especially that applications to climate and combustion require frequency dependent coefficients and coupling with the Navier-Stokes equations. Nevertheless, by using a formulation due to Chandrasekhar, existence and uniqueness can be established as a limit of an increasing sequence with very few constraints on the coefficients. The same property leads to a fast numerical algorithm with a ray-tracing type step and a convolution step accelerated by the H-matrix algorithm. Numerical results will be shown for the earth atmosphere and for the effect of sunlight on Boussinesq’s instabilities in a lake.