THE EFFECT OF THE FORMULATION OF NONLINEAR TERMS ON ALIASING ERRORS IN SPECTRAL METHODS

The effect on aliasing errors of the formulation of nonlinear terms, s uch as the convective terms in the Navier-Stokes equations of fluid dy namics, is examined. A Fourier analysis shows that the skew-symmetric form of the convective term results in a reduced amplitude of the alia sing errors relative to the conservative and nonconservative forms. Th e three formulations of the convective term are tested for Burgers' eq uation and in large-eddy simulations of decaying compressible isotropi c turbulence. The results for Burgers' equation show that, while in ce rtain cases the nonconservative form has the lowest error, the skew-sy mmetric form is the most robust. For the turbulence simulations, the s kew-symmetric form gives the most accurate results, consistent with th e error analysis.