General Formulation of Second-Order Semi-Lagrangian Methods for Convection-Diffusion Problems

Abstract EN

The general formulation of the second-order semi-Lagrangian methods was presented for convection-dominated diffusion problems.

In view of the method of lines, this formulation is in a sufficiently general fashion as to include two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones.

And it is easy to be extended to higher-order schemes.

We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate.

The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed.

Finally convergence properties of the semi-Lagrangian finite difference schemes are tested.