In this presentation, we revisit the derivation of fluid dynamic equations from the Boltzmann equation. Our approach reformulates the closure of conservation equations as a variational multiscale problem [1], encompassing established methods such as the Chapman–Enskog expansion. Within this framework, we obtain closures that extend the Navier–Stokes–Fourier equations in both linear and nonlinear regimes [2]. We then apply the linearized version of this extension to two benchmark problems—the stationary heat transfer problem and Poiseuille flow—and compare our analytical results with asymptotic and numerical solutions of the linearized Boltzmann equation. In both cases, our extended model captures the transition regime with remarkable accuracy, and for some macroscopic variables, this agreement persists well beyond that regime. REFERENCES [1] Hughes TJR, Feijóo GR, Mazzei L, Quincy JB (1998). The variational multiscale method—a paradigm for computational mechanics. Computer methods in applied mechanics and engineering, 166(1-2), 3-24. [2] Baidoo FA, Gamba IM, Hughes TJR, Abdelmalik MRA (2026). Extensions to the Navier–Stokes–Fourier equations for rarefied transport: Variational multiscale moment methods for the Boltzmann equation. Mathematical Models and Methods in Applied Sciences, 36(01):111-72.