Simulation of viscous flows with boundary layers within multiscale model using generalized hydrodynamics equations

Abstract

The multiscale method for computational fluid dynamics (CFD) is proposed to solve viscous flow problems at high Reynolds numbers with a thin boundary layer. This method is a physics-based model, uses generalized hydrodynamic equations proposed by Alexeev (1994), and can be interpreted as a regularization of the Navier-Stokes equations. Numerical solutions using this approach compare favorably with experimental data for the cases we considered for different flow problems in the range of Reynolds number from Re $=$ 3200 to 1,000,000. The method is discussed and numerical solutions are compared with the experimental data for a 3D driven cavity flow at Re $=$ 3200 and 10,000, 2D backward facing step flow at Re $=$ 44,000, 2D channel flow at Re number up to $10^6$; and a 3D thermal convection in a cylinder at Ra = 1000 to 150,000. Comparison with the analytical asymptotic solution is provided for a thermal convection, in the electrically conducting fluid suppressed by a strong magnetic field at Hartman numbers Ha up to 20,000. This multiphysics model is not a turbulence model, and no additional equations are introduced. Kinetic effects (small flow scales) are successfully captured with new terms introduced into the governing equations, and the derived small scale of turbulence compares well with observed in the experiments by Koseff and Street (1984).