Topology optimization of fluid domains: kinetic theory approach

摘要: We consider the problem of optimal design flow domains for Navier-Stokes flows in order to minimize a given performance functional. attack using topology optimization techniques, or control coefficients, which are widely known structural elastic solids and structures their flexibility, generality, yet ease use, integration with existing FEM software. use simple kinetic model approximate system. Arguably, we take rather unconventional path theory, it only gain insight about Navier-Stokes-related system hydrodynamical equations, as our starting point. Thus all modifications make models "hydrodynamically" inspired seek no particular physical explanation them; requirement us is convergence (at least, formal) equations towards correct limit. formally compute limit proposed system, rigorously establish existence solutions continuous dependence on parameters. Optimal controls shown belong special class (0-1 solutions) popular power dissipation minimization viscous fluids.