**4.2 2DV boundary layer model**

Equations (50) to (54) are easily solved applying an implicit finite-difference approach centred in space and forward in time. The alternating direction implicit (ADI) method is used to solve the equations for and *K*. The Poisson equation for is solved by the bloccyclic reduction method (Roache, 1976), which allows a huge saving in calculation time compared to the Gauss-Seidel iteration method (Huynh-Thanh & Temperville, 1991). Final solution is obtained iteratively during the time-period *T* of the signal introduced at the upper limit of the boundary layer. A flowchart representing the numerical solution implemented is presented in figure 4.

Fig. 4. Flowchart for the 2DV one-equation *K L* boundary layer model

Comparisons of laboratory experiments with numerical results of the 2DV boundary layer model are presented later, in section 6.
