| 講演要旨： |
We will present a new kinetic-fluid methodology. It relies on the introduction of a buffer zone, where a fictitious mixture model is used. The derivation of the model is based on asymptotic theory. The resulting coupling methodology has several advantages:
- The kinetic-fluid interface is described by a cut-off function which physically represents the volume fraction of one of the model (say the kinetic one) in the overall mixture
- There is no mesh adaptation required to follow the interface in case of adaptive methodology. The cut-off function can be evolved like any other variable
- There is no need to define boundary conditions at the end of the fluid or kinetic region. The transfers between the two models are taken care of by convenient source terms.
We shall present two variants of the method. The second one is targeted at making it usable for localized model upscaling (i.e. the algorithm is able to detect a region where the kinetic model must be used instead of the fluid one, and locally upscales the model accordingly). Several examples of applications will be presented, coupling kinetic with diffusion models (e.g. neutron transport, radiative transfer) and with fluid models (e.g. Euler-BGK coupling or Burgers-Jin-Xin models) in one and two dimensions. An account of moving kinetic region will be given (work in progress with G. Dimarco).
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