High-order implementation of the kinematic Laplacian equation method by spectral elements

A novel high-order implementation for the Navier–Stokes equations in the vorticity–velocity formulation is presented. It is based on the kinematic Laplacian equation (KLE) method introduced in a previous work as a low-order finite-element approach. Different aspects of the high-order implementation by spectral elements of this novel procedure are discussed. The well-known problem of a semi-infinite region of stationary fluid bounded by an infinite horizontal flat plate impulsively started is used in different ways to conduct comparative evaluation tests. This time dependent boundary-layer-development problem has an exact analytic solution, and may be regarded as a canonical problem for the subject of generation of vorticity boundary conditions in vorticity–velocity approaches. Results are analyzed and conclusions presented.

► We present a high-order implementation for the vorticity–velocity NS equations.
► High-order implementation by spectral elements of this novel procedure is discussed.
► The problem of a flat plate impulsively started is used to conduct evaluation tests.
► Boundary layer evolution and generation of vorticity boundary conditions are analyzed.