Comparison of Truncation Errors in Eulerian and Lagrangian schemes.
by
Russel P. Morison
Centre for Environmental Modelling and Prediction (CEMAP), UNSW
Coauthors: Lance M. Leslie (CEMAP, UNSW), Lixin Qi (CEMAP, UNSW)

In Numerical Weather prediction currently there is an ongoing debate concerning the merits of Eulerian and Semi-Lagrangian schemes for solving the Euler equations. Both schemes have their advocates and detractors. The debate was stimulated originally by several studies suggesting that semi-Lagrangian schemes were inherently superior to Eulerian schemes. The evidence presented was based largely on standard simulations of convective bubbles. However the comparisons were made using different orders of accuracy in the different schemes. The Semi Lagrangian schemes were normally order 3 accurate, which was higher than the Eulerian schemes which were normally order 2 accurate.

It is shown here, over a wide range of numerical problems that when the schemes were chosen to be of equal order the results were virtually indistinguishable. Our contention is that it is the order of the scheme that is paramount , not whether the scheme is Eulerian or semi-Lagrangian, in determining the accuracy of the simulations. Therefore, choice of scheme should be based on other considerations, such as : Computer architecture choice, CFL criteria, CPU availability etc .

Date received: July 29, 1999