Hyperbolic advection-diffusion schemes for high-Reynolds-number boundary-layer problems

This paper discusses issues in hyperbolic advection-diffusion schemes for high-Reynolds-number boundary-layer problems. Implicit hyperbolic advection-diffusion solvers have been found to encounter significant convergence deterioration for high-Reynolds-number problems with boundary layers. The problems are examined in details for a one-dimensional advection-diffusion model, and resolutions are discussed. One of the major findings is that the relaxation length scale needs to be inversely proportional to the Reynolds number to minimize the truncation error and retain the dissipation of the hyperbolic diffusion scheme. Accurate, robust, and efficient boundary-layer calculations by hyperbolic schemes are demonstrated for advection-diffusion equations in one and two dimensions.