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Abstract: We consider in this paper the initial-boundary value problem for the 1D neutron transport equation with isotropic scattering, set in some bounded interval with inflow boundary conditions. The usual parabolic scaling yields the diffusive limit. A surrogate model, coupling transport and diffusion equations, is then introduced in order to accurately assess the value of specific quantities of interest. The control of the quality of the computation (with respect to such a quantity of interest) is performed by means of an approach for modeling error estimation combined with an adaptive strategy to control the surrogate model, if necessary. [Copyright &y& Elsevier]

Abstract: We present the various levels of possible modeling for multiphase flows: coupling of fluid equations in different domains with a free boundary; coupling (in the same domain) of a fluid equation and a kinetic (Vlasov or Vlasov–Boltzmann) equation; coupling (in the same domain) of two (or more) fluid equations. We briefly present the mathematical results relative to the passage from one of these approaches to another approach, and we give some ideas of how to use those different models on a specific practical example. [Copyright &y& Elsevier]