Adaptive finite element simulations of the surface currents in the North Sea Original Research Article

The Navier-Stokes equations are solved for the pressure and flow of the surface currents in the North Sea. The solution algorithm applied is the nodal adaptive mesh and adaptive time method. The Navier-Stokes equations are split in four equations which are solved sequentially. The first equation, which is solved implicitly, is the diffusion equation. The second equation, which is solved explicitly, is the convection equation. The third equation, which is solved implicitly, is the pressure correction equation and the fourth equation, which is solved explicitly, is the velocity correction equation. The two equations, the diffusion and the pressure correction equation which are solved implicitly, are symmetric, linear and positive definite. The implicit equations are therefore solved by a symmetric conjugate gradient algorithm.