A multiscale kinetic–fluid solver with dynamic localization of kinetic effects

This paper collects the efforts done in our previous works 7, 9 and 10 to build a robust multiscale kinetic–fluid solver. Our scope is to efficiently solve fluid dynamic problems which present non-equilibrium localized regions that can move, merge, appear or disappear in time. The main ingredients of the present work are the followings ones: a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary; this multiscale description of the flow is obtained by using a micro–macro decomposition of the distribution function [9]; the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function; to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself. Several numerical examples are presented to validate the method and measure its computational efficiency.