Q2. What are the methods used in realistic 3-D models?
The methods generally used in realistic 3-D models are relaxation methods, and/or a Flather condition for the free surface, and radiation conditions for the other variables.
Q3. What is the common way to overcome this problem?
The most common way to overcome this problem consists in adding some numerical viscosity at the boundary, which produces a non physical boundary layer.
Q4. What is the main reason for the separation into vertical modes?
The separation into vertical modes relies on a strong but necessary hypothesis, which is that the linearization of the equations must be done around a barotropic velocity.
Q5. What is the basic idea in the preceding method?
The basic idea in the preceding method consists in choosing for OBCs the original set of model equations with as few approximations as possible.
Q6. What is the originality of Röed and Cooper's method?
Note however that the originality of their method lies also in the fact that the transient component L′k is assumed to be advected by the mean flow, and can thus be computed by upwind schemes when the mean flow is directed outwards.
Q7. What is the fundamental point of the hyperbolic open boundary problem?
A fundamental point is that, for a hyperbolic open boundary problem to be well-posed, one must prescribe as many boundary conditions as the number of incoming characteristics.
Q8. What is the first method for calculating w3 on the open boundary?
A first method consists in computing the values of w3 on the open boundary by solving the preceding equation using upwind schemes for the normal derivative ∂w3/∂x.
Q9. What is the way to compute outgoing quantities?
Therefore a natural method is to specify information on incoming characteristic variables only, and to compute outgoing quantities from interior values, using for instance upwind schemes.
Q10. What is the basic reason for these results?
The basic reason for these results is the explanation given previously, indicating that the Sommerfeld condition is justified only in the context of wave equations with a constant phase velocity.