In this note we consider the development of a domain decomposition scheme directly obtained from the multiscale hybrid scheme described in [7]. The basic idea is to couple macroscopic and microscopic models in all cases in which the macroscopic model does not provide correct results. We will show that it is possible to view a Boltzmann–Euler domain decomposition method as a subset of the hybrid scheme [7], if we impose the value of the relaxation parameter equal to zero in some regions of the computational domain. Applications to the two-dimensional BGK equation is presented to show the performance of the method.
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Dimarco, G., Pareschi, L. (2008). Domain Decomposition Techniques and Hybrid Multiscale Methods for Kinetic Equations. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_43
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