ISSN:
0363-9061
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Architecture, Civil Engineering, Surveying
,
Geosciences
Notes:
The evolution of a gravity-driven free-surface flow of varying horizontal extent which couples with a field evolving within the flow is solved using a finite difference discretization of a mapping of the problem onto the unit square. Since the size of the solution domain may show several orders of magnitude of variation, while the normalized geometry of the domain and the internal field may not vary significantly, this procedure avoids excessively fine or coarse discretizations, as well as interpolations at the boundary.The parabolic and hyperbolic evolution equations for the internal field are considered. The evolution of the coupled system is solved by an implicit marching scheme. The discretizations in space and in time are accurate to second order. Multipoint upwinding is used to avoid an instability arising advective terms are large.The evolution equations are nonlinear, and are solved using a nested Newton-Raphson procedure. The nesting is achieved by using successively better approximations to the ture evolution equations. The matrix equation that arises is solved by a conjugate-gradient-like (ORTHOMIN) iteration procedure with an incomplete Cholesky factorization preconditioning.The method has a wide variety of potential applications in the earth sciences, with the ability to describe glacier flow, lava flow, avalanching and landslides. Some calculations of the thermomechanical evolution of ice-sheets are given as illustrations, and the possible existence of thermally induced instabilities is considered.
Additional Material:
6 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nag.1610120407
Permalink
