Intercomparison between finite element and finite volume approaches to model North Sea tides

Abstract

Unstructured meshes suggest a number of advantages in tide modeling by resolving coastlines and providing refinements where it is required. We investigate the performance of several unstructured grid methods (finite element and finite volume) and time stepping schemes with respect to their accuracy and computational cost in simulating the M 2 tide in the North Sea. On a triangular mesh, we compare solutions of one finite volume and two finite element approaches ( P 1 - P 1 , P 1 NC - P 1 ) with the amplitude and phase of observation data. All models show reasonable agreement and we explain the differences. By comparing CPU times for one tidal cycle we get the computational efficiency of the temporal discretization schemes (Euler semi-implicit, leapfrog explicit, Runge–Kutta and Adams–Bashforth). Although numerical solvers involve more computational loads per time step, we give the preference to the semi-implicit models, as the increased time step size reduces the total computational time considerably.