Numerical simulation of three-dimensional free surface flow in isopycnal co-ordinates

In this paper a semi-implicit method for three-dimensional circulation in isopycnal co-ordinates is derived and discussed. It is assumed that the flow is hydrostatic and characterized by isopycnal surfaces which can be represented by explicit, single-valued functions. The hydrostatic pressure is determined by using the conjugate gradient method to solve a block pentadiagonal linear system. The horizontal velocities are determined by solving a large set of tridiagonal systems. The stability of the resulting algorithm is shown to be independent of the surface and internal gravity wave speeds.