Section:
New Results
A boundary matching micro-macro decomposition for kinetic equations
Participant :
Florian Méhats.
In [32] , we introduce a new micro-macro decomposition of collisional kinetic equations which naturally
incorporates the exact space boundary conditions. The idea is to write the distribution fonction in all its domain
as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with ) and a
reminder kinetic part. This Maxwellian is defined such that its 'incoming' velocity moments coincide with the
'incoming' velocity moments of the distribution function. Important consequences of this strategy are the following. i)
No artificial boundary condition is needed in the micro/macro models and the exact boundary condition on is
naturally transposed to the macro part of the model. ii) It provides a new class of the so-called 'Asymptotic
preserving' (AP) numerical schemes: such schemes are consistent with the original kinetic equation for all fixed
positive value of the Knudsen number , and if with fixed numerical parameters
then these schemes degenerate into consistent numerical schemes for the various corresponding asymptotic fluid
or diffusive models. Here, the strategy provides AP schemes not only inside the physical domain but also in the
space boundary layers. We provide a numerical test in the case of a diffusion limit of the one-group transport
equation, and show that our AP scheme recovers the boundary layer and a good approximation of the theoretical
boundary value, which is usually computed from the so-called Chandrasekhar function.