COMPARING SCHEMES FOR INTEGRATING THE EULER EQUATIONS

Over the years there have been a number of studies comparing the relat ive merits of semi-Lagrangian and Eulerian schemes. These studies, whi ch continue to appear in the literature up to the present, almost inva riably conclude that semi-Lagrangian schemes are superior in accuracy, and produce less noise, than Eulerian schemes. It is argued in this n ote that such conclusions are not justified because they have compared semi-Lagrangian and Eulerian schemes of different orders of accuracy. Typically, the semi-Lagrangian schemes tested have employed cubic spa tial interpolation (and therefore are third order) in space, whereas t he Eulerian schemes have usually been second order (and sometimes four th order) in space. It is shown here that when semi-Lagrangian and Eul erian schemes of the same order are applied to the test case, namely, that of ''warm bubble'' convection, there are almost indiscernible dif ferences between the simulations. The contention presented here, there fore, is that it is the order of the scheme that is of primary importa nce, not whether it is semi-Lagrangian or Eulerian.