An intercomparison between finite difference and finite element (TELEMAC) approaches to modelling west coast of Britain tides

A finite element model (namely TELEMAC) with a range of mesh refinements and assumptions of coastal water depths is used to determine an optimal mesh for computing the M-2 tide in a region of significant geographical extent. The region adopted is the west coast of Britain covering the Irish and Celtic Seas. The nature of the spatially varying topography and tidal distribution, together with a comprehensive set of measurements and existing accurate finite difference model makes it ideal for such a study. Calculations show that a water-depth dependent criterion for determining element size gives an optimal distribution over the majority of the region. However, local refinements in narrow channels such as the North Channel and Bristol Channel are required. Although the specification of a zero coastal water depth, leads to a fine near coastal grid, this does not yield the most accurate solution. In addition the computational cost is high. In practice in a large area model the use of a non-zero coastal water depth yields optimum accuracy at minimal computational cost. However, calculations show that accuracy is critically dependent upon nearshore water depths. Comparison with the finite difference model shows that the bias in elevation amplitude in the finite difference solution is removed in the finite element calculation.