Font Size: 

Boundary layer will be produced if the Reynolds number of the Navier-Stokes (N-S) equations is sufficiently high. There is a large variety of numerical methods that are used to solve the flow problems to which boundary layer theory is applied, such as the Runge-Kutta discontinuoud Galerkin (RKDG) method. However, as the thin thickness and large slope of the boundary layer, the traditional RKDG method based on piecewise polynomial approximation space may not provide the best approximation to the solution and the tangential derivative value in the boundary layer unless a very fine spatial grid is divided. Nevertheless, for the high dimensional problem, the cost of computational grids is unbearable.In this presentation, based on the approximate analytic solutions of the steady compressible N-S equations, we provide the non-polynomial approximation space for solving the compressible N-S equations with high Reynolds number inside the boundary layer. For the computational region outside the boundary layer, we still use the RKDG method based on the traditional polynomial basis functions to solve it. Numerical experiments show that compared to the traditional RKDG method, this hybrid RKDG method can yield better results in a coarse mesh.