The report summarizes the work performed at the Department of Mathematics, during the first year of the European research project GITEC-TWO (contract ENV4-U96-0297). Some of the result will subsequently be published elsewhere in a more complete form. We start with the brief presentation of hydrostatic and dispersive long wave equations, in Eulerian as well as Lagrangian description, and a family of somewhat related numerical techniques.
The effect of dispersion on the 1969 tsunami, originating in deep sea south-west of Portugal, is extensively discussed in relation to numerical solutions and discretization errors. We find strong indications that dispersive effects are significant for this tsunami.
In the project work emphasis has been put on the analysis of numerical methods by analytic tools. To the knowledge of the writers this is a new approach. First an optical theory for discrete waves is established. Then the effects of a staircase boundary on run-up is investigated through separation of variables in a non-orthogonal coordinate system.
Two finite element model are presented: a technique for solution of the Boussinesq equations in Eulerian coordinates and a run-up model in Lagrangian description. The latter is verified through comparison to analytic results and a previously developed finite difference method. The results are promising.