A fundamental approach to the problem of domain decomposition in structured grid generation

A new approach is presented for the automation of structured grid generation in multiply-connected domains. In this approach, the domain decomposition problem is cast as a classical boundary value problem in which the mesh topology is defined through the imposition of appropriate boundary conditions on the domain boundaries. The automation of the domain decomposition process is achieved by transferring it from the physical space to the topological space, where it is amenable to a rigorous solution. Once the domain is decomposed in the topological space, the mesh is generated in the physical space via the solution of a non-linear elliptic partial differential operator which takes into account the curvature of the physical space. The forms of the decomposition surfaces are obtained as part of the solution of the differential operator. The latter is solved iteratively in a system of overlapping sub-domains in which the decomposition surfaces are left floating, and in which only the shape of the domain boundaries and the point distribution thereon influence the form of the final mesh.; It is shown that the proper representation of domain curvature is an essential element to the success of the domain decomposition strategy. In any curved space, the curvature of the decomposition surfaces must closely mirror the curvature of the space in order to yield a high quality mesh. Since the decomposition of the multiply-connected domain is done in the topological space, the curvature of the physical space must be re-injected into the system through the solution of an appropriate differential operator. A new mathematical formulation is derived for this purpose and takes the form of a new forcing function in the elliptic grid generation equations. This new Curvature term is completely general and can be applied to both two- and three-dimensional domains of arbitrary shape.; The combination of the new grid generation equations and the domain decomposition strategy provides a methodology for generating structured meshes in multiply connected domains without the requirement of a manual decomposition of the space. (Abstract shortened by UMI.)...