Laguerre Simulation of Boundary Layer Flows: Conditions at Large Distance from the Wall

In this contribution, a fully spectral projection method for simulating the flow over a flat plate is presented. The incompressible Navier-Stokes equations are integrated in time using a second order fractional step method, while suitable Legendre and Laguerre polynomial basis functions are combined with a Fourier expansion in the spanwise direction to represent the spatial dependence in the truly unbounded domain. An original feature of the proposed method is the treatment of the asymptotic free-stream condition far from the wall on the normal velocity component by a Petrov-Galerkin method. Convergence tests assess the spectral accuracy of the proposed method in space and its second order accuracy in time. Results from the first large scale, with30 millions of unknowns, simulation of boundary layer flow exploiting Laguerre polynomials are also reported.