HHO Methods for the Incompressible Navier-Stokes and the Incompressible Euler Equations

Abstract We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to Reynolds number. While both rely on a HHO formulation of viscous term, pressure-velocity coupling is fundamentally different, up point that approaches can be considered antithetical. The first method kinetic energy preserving, meaning skew-symmetric discretization convective term guaranteed not alter balance. approximated velocity fields exactly satisfy divergence free constraint continuity normal component weakly enforced mesh skeleton, leading H-div conformity. second scheme relies Godunov fluxes coupling: Harten, Lax van Leer Riemann Solver designed cell centered formulations adapted hybrid face formulations. resulting numerical robust inviscid limit, it applied seeking approximate solutions Euler equations. schemes are numerically validated performing steady unsteady dimensional test cases evaluating convergence rates h -refined sequences. In addition standard benchmark flow problems, specifically conceived conducted studying error behaviour when approaching limit.