In this thesis we develop and analyze a
Galerkin-Characteristic method to integrate the potential
vorticity equations of a baroclinic ocean. The method proposed
is a two stage inductive algorithm. In the first stage the
material derivative of the potential vorticity is approximated
by combining Galerkin-Characteristic and Particle methods.
This yield a computationally efficient algorithm for this
stage. Such an algorithm consists of updating the dependent
variable at the grid points by cubic spline interpolation at
the foot of the characteristic curves of the advective
component of the equations. The algorithm is unconditionally
stable and conservative for Δt = O(h). The error analysis with respect to L² -norm shows that the algorithm converges with
order O(h); however, in the maximum norm it is proved that for
sufficiently smooth functions the foot of the characteristic
curves are superconvergent points of order O(h⁴ /Δt).
The second stage of the algorithm is a projection of
the Lagrangian representation of the flow onto the Cartesian
space-time Eularian representation coordinated with
Crank-Nicholson Finite Elements. The error analysis for this
stage with respect to L²-norm shows that the approximation
component of the global error is O(h²) for the free-slip boundary condition, and O(h) for the no-slip boundary condition. These estimates represent an improvement with respect to other estimates for the vorticity previously
reported in the literature. The evolutionary component of the
global error is equal to K(Δt² + h), where K is a constant that depends on the derivatives of the advective quantity along the Characteristic. Since the potential vorticity is a quasi-conservative quantitiy, one can conclude that K is in general small. Numerical experiments illustrate our theoretical results for both stages of the method. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/30561 |
| Date | January 1990 |
| Creators | Bermejo, Rodolfo |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
Page generated in 0.0022 seconds