Several advection experiments were conducted to test semi-Lagrangian schemes and Eulerian Warming-Kutler-Lomax (WKL) algorithms. The Eulerian WKL algorithms, as a special case of fourth-degree (order) Lagrange interpolation, exhibit unacceptable results in severe tests. Split semi-Lagrangian schemes using odd-order Lagrange interpolation are stable in the long-term deformation test, while the split even-order ones are unstable. This result suggests the superiority of odd-order Lagrange interpolation to even-order Lagrange interpolation used for semi-Lagrangian advection. Split cubic spline and cubic B spline are able to preserve a sharp-shaped box after long-term revolution with good accuracy comparable to those for fifth- and seventh-order Lagrange interpolations, but the spline interpolations exhibit strong numerical instability in the deformation test.
