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, such as the convective terms in the Navier-Stokes equations of fluid dynamics, is examined. A Fourier analysis shows that the skew-symmetric form of the convective term results in a reduced amplitude of the aliasing errors relative to the conservative and nonconservative forms. The three formulations of the convective term are tested for Burgers' equation and in large-eddy simulations of decaying compressible isotropic turbulence. The results for Burgers' equation show that, while in certain cases the nonconservative form has the lowest error, the skew-symmetric form is the most robust. For the turbulence simulations, the skew-symmetric form gives the most accurate results, consistent with the error analysis.