Modified wavenumber and aliasing errors of split convective forms for compressible flows

The spectral characteristics of split convective forms for compressible flows in finite difference methods are studied. It has been widely argued that the split forms are capable of reducing aliasing errors, based on the studies that consider spectral methods. However, the theoretical analysis shown here reveals that the split forms do not reduce aliasing errors in finite difference methods but rather increase aliasing errors more than the divergence form. This is because the modified wavenumber of the split forms may not become zero at the Nyquist wavenumber and is larger than that of the divergence form in the high wavenumber range. Correspondingly, this study also concludes that the superior numerical stability of kinetic energy preserving or kinetic energy and entropy preserving schemes, in which the split forms are used, is due to the enhanced preservation property of the kinetic energy and entropy and not the reduction of aliasing errors in finite difference methods. The spectral characteristics shown in the numerical tests are in good agreement with the theoretical analysis performed in this study.