Lw. Morland et R. Staroszczyk, A MATERIAL COORDINATE TREATMENT OF THE SEA-ICE DYNAMICS EQUATIONS, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 454(1979), 1998, pp. 2819-2857
Citations number
20
Categorie Soggetti
Multidisciplinary Sciences
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
A finite-element algorithm is constructed for a material coordinate fo
rmulation of the equations of sea-ice dynamics, using quadratic elemen
ts and fully implicit time steps. The material coordinate description
allows the nodes of a fixed finite-element mesh to define the same mat
erial elements as time proceeds, which avoids interpolation of nodal v
alues on a changing spatial mesh as the pack evolves, quadratic elemen
ts preserve continuity of second derivatives, and this time stepping i
s stable and accurate in standard problems. An earlier finite-element
study of a wind-driven pack with two free boundary sections, using spa
tial coordinates and implicit time steps without iteration, gave rise
to numerical instability when the constitutive law for the ice stress
induced by floe interactions imposes zero stress in diverging flow. Th
e present more accurate study of the same problem, using a material de
scription and fully implicit time steps, with a smoothed transition to
zero stress in diverging flow, significantly extends the time over wh
ich a stable solution is obtained. Stability and accuracy of the prese
nt algorithm is first demonstrated by comparison with a class of exact
solutions to specific problems using linearly viscous relations in co
nverging flow and abrupt transition to zero stress in diverging flow,
for which an expanding region of diverging flow is initiated after a f
inite time at an interior point, either following convergence everywhe
re, or following an expanded region of neutral flow. The previous prob
lem with two free boundary sections is then solved with the same rheol
ogy to demonstrate a stable solution over an extended time period. Nex
t, a general nonlinearly viscous relation is constructed which ensures
that the stress lies close to a yield envelope during strongly conver
ging flow, to reflect the commonly used viscous-plastic model without
the disjoint stress relations in different regimes. This is applied to
a pack flow with a dramatically deforming free boundary driven by a v
ortex wind, which demonstrates how well the present material formulati
on can capture large deformations.