Computational methods for multi-domain geophysical flows.

Approximate methods for multi-domain computation of incompressible flows with a free surface are developed and tested. A semi-implicit model is constructed and applied to the computation of surface waves and gravity currents. The model includes an adaptation of the constrained interpolation method to staggered grids. A new averaging scheme is introduced for the conversion of corner point velocities to cell-centered values, and a weighting scheme is proposed to account for large variations of the advection velocity. The concept of adjustable hydrostatics is introduced and is shown to produce satisfactory results in nearly-hydrostatic flows providing significant computational savings. Although the solution of the pressure-Poisson equation is not exact, a conservative velocity field is obtained. This is a powerful tool in cases where computational speed is a factor and the flow conditions allow the associated approximation. Two new methods are developed for multi-domain computations. First, an explicit interface is developed based on sequential regularization. An initial-value problem is solved at the interface between computational domains, so no information needs to be exchanged in the form of boundary conditions between the subdomains. The second interface is based on a Receding Boundary Method. By continuously moving the overlapping boundaries between subdomains, the method is able to reduce the errors introduced by the use of an open boundary condition at the common boundary. This eliminates the need for communication during each time step, and allows for an independent solution in the two subdomains. The results are accurate and the communications can be reduced by a factor of 5-10 times. The technique is extended to three space dimensions and in analysis of its behavior is conducted by numerical experimentation.Ph.D.Applied SciencesCivil engineeringEarth SciencesGeophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126459/2/3253306.pd