Spectral-Element Implementation Of The Kle Method: A (!, V ) Formulation Of The Navier–Stokes Equations

Abstract

The kinematic Laplacian equation (KLE) method is a novel procedure belonging to the
vorticity-velocity (!, v) family known as the hybrid formulation of the Navier–Stokes equations. The
results of its early classical FEM implementation exhibited satisfactory agreement with experimental
measurements. However, thinking on future implementations of the KLE method, it is worth to know
its behavior with different space and time discretization techniques. To this end, we started a systematic
analysis of the particularities of a high-order implementation of the KLE by spectral-element techniques.
Different aspects of the high-order implementation by spectral elements of this novel procedure are discussed
in this work. 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-dependant boundary-layer-development problem has an exact analytic solution,
allowing to compare the numerical solution against it. Results are analyzed and conclusions presented.