Challenges in numerical simulations Modern cfd: Based on Navier-Stokes equations Efficient for continuum flows does not work for other regimes Particle Methods: (MD, DSMC.) · noise · Small time and cell size Difficult for continuum flows /low-speed non-equilibrium flows Method based on extended hydrodynamic models: Theoretical foundations Numerical difficulties( Stability boundary conditions Limited to weak-nonequilibrium flowsChallenges in numerical simulations • Based on Navier-Stokes equations • Efficient for continuum flows • does not work for other regimes • Noise • Small time and cell size • Difficult for continuumflows / low-speed non-equilibrium flows Modern CFD: Particle Methods: (MD, DSMC… ) • Theoretical foundations • Numerical difficulties (Stability, boundary conditions,……) • Limited to weak-nonequilibrium flows Method based on extended hydrodynamic models :