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This paper collects the efforts done in our previous works [P. Degond, S.Jin, L. Mieussens, A Smooth Transition Between Kinetic and HydrodynamicEquations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L.Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J.Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L.Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects,SIAM Multi. Model. Sim. 5(3), 940--979 (2006)] to build a robust multiscalekinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problemswhich present non equilibrium localized regions that can move, merge, appear ordisappear in time. The main ingredients of the present work are the followingsones: a fluid model is solved in the whole domain together with a localizedkinetic upscaling term that corrects the fluid model wherever it is necessary;this multiscale description of the flow is obtained by using a micro-macrodecomposition of the distribution function [P. Degond, J.G. Liu, L. Mieussens,Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi.Model. Sim. 5(3), 940--979 (2006)]; the dynamic transition between fluid andkinetic descriptions is obtained by using a time and space dependent transitionfunction; to efficiently define the breakdown conditions of fluid models wepropose a new criterion based on the distribution function itself. Severalnumerical examples are presented to validate the method and measure itscomputational efficiency.

A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects