An Investigation of the Monotonicity Properties of BDF Schemes for Scalar Advection over Dynamic Meshes with Edge-Swapping

The monotonicity-preserving properties of Backward Differencing Formulae are investigated here in connection with the integration in time of the system of Ordinary Differential Equation obtained from the space discretization of the two-dimensional scalar advection equation. The space discrete equations are obtained by means of a standard finite volume scheme for unstructured triangular grids. Similarly to the one-dimensional case, an upper boundary for the Courant number is found which prevents the appearance of new extrema in the solution. For the considered cases, the maximum Courant number is found to be around 0.5, a value that is comparable to that obtained from the one-dimensional theory. These findings applies also to dynamic grids with edge-swapping, in which the advection equation is solved by means of an Arbitrary Lagrangian Eulerian approach.